Papers

Let $K^h$ be a Henselization of a valued field $(K,v),$ $w$ a valuation-transcendental extension of $v$ to $K[x],$ and $\phi$ a key polynomial for $w$. In this paper, we prove that if $\phi$ is irreducible over $K^h,$ then the simple extension $L|K,$ generated by a root of any key polynomial for $w,$ is unibranched and its defect is independent of the choice of key polynomial. As a consequence, we generalize some well-known results for Henselian valued fields to arbitrary valued fields. Moreover, we provide some criteria for $L|K$ to be unibranched and defectless in terms of Mac Lane-Vaquié chains, complete sequences of abstract key polynomials and saturated distinguished chains. As an application, we generalize a classical result of Ore about the existence of $p$-regular generators for number fields.

By exploiting complex coordinates and elementwise matrix products, a single and simple differential equation is derived that describes the motion of every multi-arm planar pendulum.

The (binary) differential-linear connectivity table (DLCT) measures the dependence between an input difference and a linear mask applied to the corresponding output difference. For vectorial Boolean functions, each DLCT entry is one half of an additive autocorrelation value. We extend this relation to functions over finite fields of arbitrary prime characteristic by introducing a level-resolved p-ary differential-linear profile. Its entries are the centered numbers of inputs for which a derivative component has each prescribed trace value in $\mathbb{F}_p$. The discrete Fourier transform of this profile is the family of additive autocorrelations obtained by multiplying the output mask by the nonzero elements of $\mathbb{F}_p$; when p=2, the usual binary identity is recovered. For a fixed input difference, we show that the profiles over all nonzero output masks determine the corresponding DDT row exactly, and we give an explicit inversion formula. We establish a second-moment identity: the total profile energy in one derivative direction is a constant multiple of the squared Euclidean distance between that DDT row and the balanced row. Thus this energy is determined by the full row differential spectrum, not by differential uniformity alone. It follows that all profiles in a direction vanish exactly when the derivative is balanced; for square maps in odd characteristic, this gives a characterization of planarity. As concrete odd-characteristic examples, we determine the complete profile of the monomial $x^{p^k+1}$ and derive an exact Kloosterman-sum formula for the inverse monomial. Finally, we determine the behavior of the profiles under equivalence. EA-equivalence reindexes the input and output masks and translates the trace level, whereas a general CCZ equivalence may mix several derivative directions. Nevertheless, for square maps the global nontrivial profile energy is CCZ-invariant.

In this paper, we establish a sharp non-uniqueness result to the semilinear wave equation \[ \partial_{tt}u-\partial_{xx} u= \Theta_1(\partial_t u)^2 + \Theta_2(\partial_x u)^2. \] For any $\Theta_1 \Theta_2 < 0$, $\beta<1$, we construct infinitely many weak solutions $u \in C_{t,x}^{\beta}$ with zero initial data. To our knowledge, this is the first non-uniqueness result for a semilinear wave equation. At this low level of regularity $C_{t,x}^{\beta}(\beta<1)$, the quadratic term is defined by Littlewood–Paley decomposition in $C_t H_x^{-s}$. Our construction is based on a frequency-localized convex integration scheme. Together with the classical local uniqueness theory in $C_{t,x}^{1}$, this non-uniqueness result is sharp.

We study absolutely $r$-summing Toeplitz operators $T_f:F_\varphi^p\to F_\varphi^q$ with complex symbols. The weight has a uniformly positive and bounded real Hessian. The main difficulty is that local distance to holomorphic functions does not detect an entire part of the symbol, while the Toeplitz operator does. Using the complete classification of absolutely summing diagonal maps, we characterize absolutely summing Fock–Carleson embeddings. An IDA decomposition, a Rademacher argument, and local scalar recovery then detect the missing analytic part of a complex symbol. We obtain equivalent criteria in terms of the local $L^q$ mean, the complex ball average, and the Berezin transform for every $1\le p,q,r<\infty$. At $q=1$ the criterion is $L^{s_p}$, where $s_p=2p/(3p-2)$ for $p\le2$ and $s_p=1$ for $p>2$. We also obtain a sectorial-symbol criterion without an IDA assumption and prove sharpness by separated models.

LCD codes over finite commutative chain rings are known to be free. However, if the ring is not indecomposable, there always exists an LCD ideal that is projective but not free. We prove that all two-sided LCD codes are projective. We generalise the characterisation of finite commutative Frobenius rings by means of the size condition of a code and its dual to the noncommutative setting. This result is applied to prove that group codes are LCD if and only if they are generated by a central idempotent.

We determine the additive structure of the integral cohomology groups with trivial coefficients of the Artin groups in the spherical families $A_n,C_n,D_n$ and the affine families $\widetilde B_n,\widetilde C_n,\widetilde D_n$. We first compute the integral cohomology of braid groups by algebraic methods and then use the Salvetti complexes to express the cohomology of the remaining families in terms of these computations. The resulting descriptions apply in every admissible rank. For each family, we establish cohomological stabilization and show that the integral cohomology groups contain no elements of order $p^2$ for any prime $p$. We also give uniform generating series formulas describing the stable integral cohomology in terms of that of the braid groups.

We show the homology cobordism group of homology $3$-spheres is not generated by graph homology $3$-spheres. Our technique is a combination of filtered instanton Floer theory and Gromov's simplicial volume.

Let $G$ be a graph on $n$ vertices, and let $e_G(S,V(G)\setminus S)$ be the number of edges with exactly one endpoint in $S$. The Cheeger constant and the restricted Cheeger constant of $G$, where $k\ge1$ is real, are, respectively, \[ h(G)=\min_{\substack{\emptyset\ne S\subseteq V(G)\\|S|\le \frac{n}{2}}} \frac{e_G(S,V(G)\setminus S)}{|S|} \text{ and } h_k(G)=\min_{\substack{\emptyset\ne S\subseteq V(G) |S|\le\min\{k,\frac{n}{2}\}}} \frac{e_G(S,V(G)\setminus S)}{|S|}. \] The contraction clique number $\ccl(G)$ is the largest integer $r$ such that $G$ contains the complete graph $K_r$ as a minor. Krivelevich and Nenadov [Complete minors in graphs without sparse cuts, Int. Math. Res. Not. IMRN 12 (2021) 8996–9015] proved that, for every fixed $\eps>0$ and all sufficiently large $n$ and $d$, if $G$ is a graph on $n$ vertices with maximum degree at most $d$, then $h(G)\ge\eps d$ and $h_{\eps n}(G)\ge(\frac{1}{2}+\eps)d$ imply $\ccl(G)=\Omega_\eps(\sqrt{\frac{nd}{\log d}})$. They asked to determine if one can guarantee the same lower bound on $\ccl(G)$ without the additional condition on $h_{\eps n}(G)$. They showed that this is the case when $d$ is a constant. We answer this question affirmatively. For every $\eps>0$, there are constants $\beta=\beta(\eps)>0$ and $n_0=n_0(\eps)$ such that, whenever $d\ge 3$ is an integer, for every graph $G$ with $n\ge n_0$ vertices and maximum degree at most $d$, if $h(G)\ge\eps d$, then $\ccl(G)\ge\beta\sqrt{\frac{nd}{\log d}}$. The dependence of this lower bound on $n$ and $d$ is best possible up to a constant factor. As a corollary, a lower bound is derived for the contraction clique number of $d$-regular graphs for which the second largest eigenvalue is bounded away from $d$, compared to earlier $\frac{d}{2}$. The proof combines spectral properties of graphs with an analysis of lazy random walks.

For an entire function $f$ and a non-zero complex number $\lambda$, let $f_\lambda(z)=f(\lambda z)$. We give conditions on $f$ which imply that the Hausdorff dimension of the set of non-escaping points in the Julia set of $f_\lambda$ tends to $1$ as $|\lambda|\to 0$. In fact, we give an upper bound for this dimension in terms of $\lambda$. This generalizes earlier results concerned with the case that $f(z)=\exp z$.

In this paper, we establish the validity of the Hilbert expansion for the coupled radiation-Euler model with non-relativistic source term for general initial data on the torus $\mathbb{T}^{3}$, which leads to the simplified equilibrium-diffusion limit and the initial layer corrections for the radiation intensity coupled with the temperature.

Chance constraints are widely used in optimization under uncertainty. This paper aims to show the eventual convexity (EV) of chance constraints with skewed generalized hyperbolic (GH) random variables. We prove that the densities of GH distributions are $\alpha$-decreasing, and obtain exact convex reformulations for separable jointly chance constraints with GH distributions. We provide numerical results to compute the $\alpha$-decreasing threshold parameters and show the EV of the feasible set together with the computational tractability to solve the associated optimization problems.

We classify geometrically nondegenerate GV subschemes of codimension three in indecomposable principally polarized complex abelian varieties of dimension $g\ge6$. Every such subscheme is a translate of $\pm W_{g-3}(C)$ in the Jacobian of a smooth curve $C$. The proof studies the theta-dual surface: tangent cones and theta Hessians give a curve summand in the singular case, while Hodge gradings and characteristic cycles give one in the smooth case. Theta duality yields the corresponding classification of GV surfaces. We also compute the cohomology of all topologically trivial twists of the ideal sheaf twisted by the principal polarization, and characterize the hyperelliptic case by a cohomology jump.

The spectral sample and pivotal set of a percolation crossing have the same one- and two-coordinate inclusion probabilities under the uniform product measure. We prove that both Shannon entropies are comparable to total influence for critical square-lattice bond and triangular-lattice site crossings, with matching estimates at every retained nonroot spatial resolution. The triangular entropy bounds are uniform over a class of inhomogeneous near-critical product measures. For critical triangular-site square crossings, the two laws are asymptotically mutually singular: an elementary triangular face is forbidden in the pivotal set and occurs with positive density in a large spectral sample. Every fixed face density below an explicit threshold has nonempty spectral probability comparable to $R^2\alpha_4(R)^2$, while the nonempty overlap of the two laws has decay exponent $11/12$. Their minimum expected symmetric-difference distance over all couplings is comparable to total influence. Geometric separation persists after independent thinning whenever the retention probability $\rho_R$ satisfies $\rho_R^3R^2\alpha_4(R)\to\infty$; the face detector fails when this quantity tends to zero. The proofs combine spatial encoding, arm estimates, local Fourier cancellation, and an exact six-cycle coercivity inequality preserved under exterior conditioning.

We establish three results on decision problems for finitely generated matrix groups, based on fiber products: $\bullet$ The torsion-freeness problem is undecidable for subgroups of $\mathrm{SL}_{4}(\mathbb{Z})$, $\bullet$ There exists a finitely generated subgroup $G$ of $\mathrm{SL}_{4}(\mathbb{Z})$ with undecidable square root problem, $\bullet$ No algorithm can, on input a tuple of invertible matrices, output the list of marked finite quotients of the group they generate.

We show that for any henselian valued field of mixed characteristic $(0,p)$, the (existential) $\mathcal{L}_{\mathrm{val}}$-theory of the valued field is determined by the (existential) theory of the value group in $\mathcal{L}_{\mathrm{oag}}$ with a constant for $v(p)$ and the (existential) theory of the residue ring $\mathcal{O}_v/(p)$ in an expansion $\mathcal{L}_{\mathrm{Witt}}$ of the language of rings, provided $\mathcal{O}_v/(p)$ is semi perfect. We moreover show that the $\mathcal{L}_{\mathrm{Witt}}$-structure on $\mathcal{O}_v/(p)$ is $\mathcal{L}_{\mathrm{ring}}$-definable using constants, and that this is exactly the structure induced on $\mathcal{O}_v/(p)$ by the ambient valued field. As a consequence, we obtain a relative quantifier elimination result (eliminating $K$-quantifiers) in a suitable language for the theory of roughly deeply ramified henselian valued fields of mixed characteristic $(0,p)$.

We show that the parabolic uniform rectifiability of a set can be characterized by an interior PDE property, namely Carleson measure estimates for bounded solutions to the heat equation. In particular, under very mild background hypotheses on an open set $\Omega$ and its boundary $\partial \Omega$, we show that the following are equivalent: (i) The quantity $|\nabla u(\cdot)|^2 \text{dist}(\cdot, \partial\Omega)$ is the density of a Carleson measure on $\Omega$ for all bounded solutions to the heat equation in $\Omega$. (ii) The caloric measure for $\Omega$ admits a corona decomposition. (iii) $\partial \Omega$ is parabolic uniformly rectifiable. The implication (iii) implies (i) is the main result of the cited paper [Bortz, Hoffman, Hofmann, Luna-García, Nyström, Anal. PDE 2023]. The remaining implications are new, and are direct parabolic analogues of results of Garnett, Mourgoglou and Tolsa [Duke Math. J. 2018] in the elliptic setting for the Laplacian; however, our proofs require several new ideas. In particular, we must adapt arguments to account both for time-lag, and for the fact that some characterizations of (elliptic) uniform rectifiability have either not been developed or have been shown to be untrue in the parabolic setting. Our background assumptions, as noted above, are very mild: we assume that the domain satisfies the time-symmetric capacity density condition and has interior corkscrews, and that the boundary is (non time-directed) Ahlfors-David regular. These are weaker than the background assumptions of Bortz, Hofmann, Martell and Nyström in arXiv:2510.22047, and are essentially optimal for the boundary continuity properties of caloric functions on which our arguments rely.

Image reconstruction in optical interferometry remains a challenging inverse problem due to sparse Fourier sampling and the strong dependence of the reconstructed images on user-defined parameters. We present PYRA (Python for MiRA) and MYTHRA (Mean Astrophysical Images with PYRA), two tools designed to improve the robustness and reproducibility of interferometric imaging. PYRA automatically generates large ensembles of MiRA reconstructions by exploring a wide range of reconstruction parameters, while MYTHRA statistically analyzes the resulting images to identify the most consistent solutions and derive a final averaged image with associated uncertainty estimates. The methodology is validated using the blind datasets of the 2024 Interferometric Imaging Contest, where our reconstruction strategy achieved the best overall score. We further apply the method to VLTI/MATISSE observations of the triple AGB system {\pi}1 Gru and the A[e] supergiant 3 Pup. These results demonstrate that statistical analysis of large reconstruction ensembles provides a powerful framework for assessing image reliability and reducing reconstruction artifacts in optical interferometry.

In 1980, Carleson posed a question about the least regularity required for initial data in a Sobolev space $H^s$ to ensure pointwise convergence of the solution to the single particle linear Schrodinger equation. In this paper, we study Carleson problem on the $d$-dimensional waveguide manifold $\mathbb R^n\times \mathbb T^m$ and initiate its analogy for the system of infinitely many orthonormal particles (arising from the transition of many-body quantum mechanics to the thermodynamic limit) on torus and waveguide manifold. For a single particle on the waveguide manifold, we establish a maximal-in-time Strichartz estimate that yields almost everywhere convergence to the initial data in $H^s$ for $s > \frac{d}{d+2}$. On the other hand, we adopt Bourgain counterexample approach to show that this convergence fails for $s< \frac{d}{2(d+1)}.$ For infinitely many particles, we generalize the classical maximal-in-time Strichartz estimate and pointwise convergence result of Compaan, Luca and Staffilani (2021) in the setting of fermionic systems on the torus. Similar result is also established for the waveguide manifold. We also establish necessary condition (in the spirit of Bourgain's counterexample) for the pointwise convergence problem for fermionic systems. These are the first results in the setting of torus and waveguide manifold, and complement the works of Bez, Lee and Nakamura (2020) and Bez, Kinoshita, Shinya and Shiraki (2024) on Euclidean space.

We study the regularity of weak solutions to doubly nonlinear orthotropic evolution equations of the form \[ \partial_{t}(\vert u\vert^{\alpha-1}u)-\sum_{i=1}^{N}\partial_{i}\left[a_{i}(x,t)\,(|\partial_{i}u|-\delta_{i})_{+}^{p-1}\frac{\partial_{i}u}{\vert\partial_{i}u\vert}\right]=f\,\,\,\,\,\,\,\,\,\,\mathrm{in}\,\,\,\Omega_{T}=\Omega\times(0,T), \] where $\Omega$ is a bounded open subset of $\mathbb{R}^{N}$ for $N\geq2$, the coefficients $a_{i}$ are measurable and bounded, $\alpha>0$, $p\in(1,\infty)$ and $\delta_{1},\ldots,\delta_{N}$ are non-negative numbers. We show that weak solutions are locally bounded due to their membership in a suitable De Giorgi-type energy class. We also obtain contractive estimates and global boundedness in space for solutions to a Cauchy problem associated with the above PDE. Our analysis extends analogous results available in the literature for diffusion equations that either do not exhibit double nonlinearity or are less degenerate than those considered here. Another main novelty of this paper is the presence of a source term $f$ on the right-hand side of the equation, for which we impose suitable integrability assumptions in the space-time variables.

We study robust Mckean-Vlasov Forxard Backward systems with jumps under a nondominated family of probability measures. The backward equation contains a lawdependent nonsmooth monotone source motivated by asymmetric loss aversion. We establish well-posedness and stability of the system, analyze its Yosida regularization, and develop quantitative particle approximations. The main difficulty comes from the discontinuity of the minimal selection across switching interfaces, which prevents the use of direct Lipschitz estimates. To overcome this difficulty, we combine forward propagation of chaos with occupation estimates for the limiting forward process. Importantly, no occupation estimate is required for the particle system. Under a second-moment occupation condition, we obtain an improved joint convergence rate for the particle and Yosida approximations, controlling the forward and backward states, the martingale integrands, and the accumulated source. We also verify the required occupation conditions for several concrete jump models, including affine stable-like dynamics, predictable variable jump amplitudes, and a non-affine class obtained by smooth conjugacy

We study optimal jump truncation for the additive time-singular pure-jump model of the form $X_T=\int_0^T t^{-\sigma} dZ_t$, where $Z$ is a Lévy process and $\sigma\ge 0$. For a fixed expected jump cost, we minimize the residual small-jump variance over measurable time-dependent cutoffs. Under regularity and tail assumptions on the Lévy measure, we prove that the problem admits an optimal cutoff, unique up to a.e. equality, of the form $r^\ast(t)=(c^\ast t^\sigma)\wedge 1$. In the symmetric $\alpha$-stable case, we obtain explicit matched-cost comparisons with the classical fixed cutoff and show that within the admissible non-truncated regime the Dynamic Cutting family is strictly better than the classical fixed cutoff whenever $0<\sigma<1/2$. Finally, for symmetric Lévy measures and cutoffs satisfying the corresponding $L^p$-integrability assumptions, we derive the weak-error bound $W_p(r)\le C_p \mathcal{E}^{p/2}(r)$, $0<p<2$, demonstrating that any cutoff which minimizes the residual variance also minimizes the corresponding upper bound for the weak error.

We introduce the notion of a directionally fine family of cones, a local geometric property expressing the possibility of selecting arbitrarily narrow cones around every direction of a normed space. We show that this local property provides a common mechanism for finite separation and approximation. In particular, directionally compact sets can be separated from closed cones by finitely many members of the family, while locally compact cones admit finite outer approximations with quantitative Hausdorff control on their sets of directions and on bounded sections. These finite constructions lead naturally to max-type positively homogeneous separators and do not require convexity of the cones to be separated. We then study two complementary realizations of the framework. For the classical family of Bishop–Phelps cones, directional fineness is characterized by the requirement that every point of the unit sphere be a denting point of the unit ball, equivalently, by property~$(G)$; in Banach spaces this amounts to rotundity together with the Kadec property. On the other hand, we introduce transversal coercivity as a general axial construction principle. It yields directionally fine families in arbitrary normed spaces, without geometric assumptions on the norm, and includes uniform axial deviation and norm-normalized axial cones as canonical models. Finally, the explicit structure of the former yields penalization and recovery results for optimization over locally compact cones, together with quantitative approximation and convergence estimates.

The Gromov hyperbolicity constant of a metric space \((X,d)\) is the infimum of all \(\delta\ge0\) such that \((X,d)\) is \(\delta\)-hyperbolic. For a Kobayashi hyperbolic domain \(\Omega\subset\C^n\) and a boundary point \(p\in\partial\Omega\), let \(\delta_{\mathrm{loc}}(\Omega,p)\) denote the local Gromov hyperbolicity constant obtained by restricting the points to arbitrarily small Euclidean neighborhoods of \(p\), while distances are still measured by the ambient Kobayashi distance \(K_\Omega\). For each even integer \(M\ge2\), let \(\mathfrak H(M)\) be the supremum of these constants over all complex dimensions \(n\ge2\) and all domains whose boundary is smooth and convex near the distinguished point and has D'Angelo type at most \(M\) at that point. We prove \[ \frac{\log 2}{2} M \le \mathfrak H(M) < 36M. \] Thus the optimal universal dependence of the local Gromov hyperbolicity constant on boundary type is linear. We also show that no analogous bound holds for the global Gromov hyperbolicity constant, even among smooth bounded strongly convex domains.

We establish a uniform quantitative comparison between the non-Archimedean Mabuchi functional and the Darvas–Zhang quantised Mabuchi functional. For a smooth polarised variety with finite automorphism group, we provide an algebraic proof that uniform $\widehat{\mathrm K}$-polystability is equivalent to uniform $\mathrm K^\beta$-stability for every sufficiently large rational $\beta>1$, without passing through the existence of a cscK metric. The main input is a square-root estimate for directional derivatives of non-Archimedean energies, proved by intersection theory. We also study a reduced $\mathrm{K}^\beta$-stability condition when the identity component of the polarised automorphism group is reductive and the Futaki character vanishes. We conclude by characterising K-semistability in terms of asymptotic $\mathrm K^\beta$-semistability and prove the quantitative convergence of the corresponding stability thresholds.

Let $\omega: \mathbb{N} \to [1, \infty)$ be a weight on the multiplicative semigroup of natural numbers. We investigate the Bochner-Schoenberg-Eberlein (BSE) property for the weighted Banach algebra of Dirichlet series $A_\omega = \ell^1(\mathbb{N}, \omega)$ under Dirichlet convolution. By employing Bohr's correspondence, we establish a weak-$\ast$ approximation framework for $\omega$-bounded semicharacters using scaled truncations that lie within the predual space $c_0(\mathbb{N}, 1/\omega)$. Utilizing the canonical $L$-projection decomposition of the bidual space $A_\omega^{\ast\ast} = A_\omega \oplus c_0(\mathbb{N}, 1/\omega)^\perp$ alongside the weak-$\ast$ compactness of the unit ball via the Banach-Alaoglu theorem, we prove that $A_\omega$ is a BSE-algebra for any weight. Furthermore, we show that the intrinsic BSE-norm on the Gel'fand transforms is isometric to the natural weighted algebra norm $\|\cdot\|_\omega$.

For integers $k\ge 1$ and $n\ge k+2$, let $g_k(n)$ be the maximum number of edges in an $n$-vertex graph containing no cycle with a vertex incident with at least $k$ chords. Erdős conjectured that $g_k(n)=(k+1)(n-k-1)$ for $n\ge 2k+2$. Lewin found a counterexample. Bollobás later conjectured that there exists a function $n(k)$ such that $g_k(n)=(k+1)(n-k-1)$ for all $n\ge n(k)$. Jiang confirmed this by proving the formula for all $n\ge3k+3$ when $k\ge1$. In this paper, we determine $g_k(n)$ completely. For all $k\ge1$ and $n\ge k+2$, we prove $g_k(n)=\big\{\lfloor\frac{(k+1)n}{2}\rfloor,\max\{a(n-a)+\lfloor\frac{a(k+1-a)}{2}\rfloor : a\in\mathbb Z,\; \lfloor {(k+1)}/{2}\rfloor+1\le a\le k+1\}\big\}$. For $k\ge2$, we prove $g_k(n)=(k+1)(n-k-1)$ when $n\ge \lceil(5k+1)/2\rceil$, and this threshold is sharp. Our proof builds on the method developed by Ma and the second author in [Ma and Ning, 2020].

We revisit Zhuravlev's 1974 quantitative form of Selberg's sign-change method for the zeros of the Riemann zeta function on the critical line. Zhuravlev's work, originally in Russian and little known in the West, established an explicit positive proportion of such zeros. Using modern techniques we optimise the arithmetic mean value at the heart of the method and obtain the strongest result yet known from Selberg's method, proving that more than $6.78\%$ of the non-trivial zeros of the Riemann zeta function lie on the critical line.

We investigate how Heegner points detect the finiteness of the $p$-primary part of Tate-Shafarevich groups of semi-stable elliptic curves over the rationals of arbitrary rank with any good reduction prime $p \geq 5$ with irreducible mod $p$ representation and partially recover Çiperiani–Wiles' theorem on solvable points on genus one curves. As a key ingredient of the proof of these results, we also give a concise proof of Kolyvagin's conjecture for semi-stable elliptic curves with supersingular reduction with a relevant choice of an imaginary quadratic field. Our approach is independent of the cyclotomic Iwasawa main conjecture for elliptic curves with supersingular reduction.

We consider the Cauchy problem for the one-dimensional full compressible Navier–Stokes equations with general constitutive laws $p=p(v,\theta)$ and $e=e(v,\theta)$. The pressure and internal energy are assumed to be sufficiently smooth, thermodynamically compatible in the sense that $e_v=\theta p_\theta-p$, and to satisfy $e_\theta>0$. We first establish the local-in-time existence and uniqueness of strong solutions for large initial data without imposing monotonicity conditions on the pressure. For perturbations around a constant equilibrium $(\bar v,0,\bar\theta)$, we further assume the mechanical stability condition $p_v(\bar v,\bar\theta)<0$. By introducing a relative thermodynamic energy through the Gibbs relation, we derive a basic energy identity and prove its local quadratic coercivity near the equilibrium. Combining this estimate with higher-order a priori bounds, we obtain the global existence and uniqueness of strong solutions for sufficiently small $H^1(\mathbb R)$ perturbations. Moreover, the specific volume and temperature remain uniformly bounded away from zero and infinity for all time.