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1. 基于高频赤道准正规模的克尔 - 德西特参数定量局部重构
Quantitative local recovery of Kerr-de Sitter parameters from high-frequency equatorial quasinormal modes
作者: Ruiliang Li
类别: math-ph, gr-qc, math.AP
发布日期: 2026-02-17
arXiv ID: 2602.15764v1
链接: http://arxiv.org/abs/2602.15764v1
摘要: We study an inverse resonance problem for the scalar wave equation on the Kerr-de Sitter family. In a compact subextremal slow-rotation regime and at a fixed overtone index, high-frequency quasinormal modes admit semiclassical quantization and a real-analytic labeling by angular momentum indices. Using this structure, we first prove that a finite equatorial high-frequency package of quasinormal-mode frequencies determines the mass and rotation parameter $(M,a)$ (for fixed cosmological constant $Λ>0$), with a quantitative stability estimate. As a key geometric input we compute explicit second-order (in $a$) corrections to the equatorial photon-orbit invariants which control the leading real and imaginary parts of the quasinormal modes. Finally, allowing $Λ$ to vary in a compact interval, we show that adding one damping observable (the scaled imaginary part of a single equatorial mode) yields a three-parameter inverse theorem: a finite package of three independent real observables determines $(M,a,Λ)$ locally in the slow-rotation regime away from $a=0$.
2. 分数阶调和映射的精细正则性及其应用
Fine regularity of fractional harmonic maps and applications
作者: Kyeongbae Kim, Simon Nowak, Yannick Sire
类别: math.AP
发布日期: 2026-02-17
arXiv ID: 2602.15715v1
链接: http://arxiv.org/abs/2602.15715v1
摘要: In this paper, we derive several regularity results for harmonic mappings into Euclidean spheres associated with rather general energies related to fractional Sobolev spaces. These maps generalize families of maps introduced by Da Lio, Rivière and Schikorra and are related to harmonic maps with free boundaries. In our context, there is in general no monotonicity formula, which prevents the use of some classical methods. Despite this limitation, under natural assumptions on a Gagliardo-type energy, we succeed in proving a variety of small energy regularity results and improve on known results, even in the isotropic case for which some monotonicity formula is available. To this end, we exploit recent developments in the regularity theory of nonlocal equations and as a by-product, we explain how these results apply to classes of harmonic maps with free boundary and lead to new potential-theoretic estimates. As another application, we obtain higher differentiability results for the fractional harmonic map heat flow.
3. 利用球化技术求解无界一致域上的狄利克雷问题
Solving Dirichlet problem on unbounded uniform domains by using sphericalization techniques
作者: Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam, Timo Takala
类别: math.AP, math.MG
发布日期: 2026-02-17
arXiv ID: 2602.15701v1
链接: http://arxiv.org/abs/2602.15701v1
摘要: Within the setting of metric spaces equipped with a doubling measure and supporting a $p$-Poincaré inequality, establishing existence of solutions to Dirichlet problem in a bounded domain in such a metric space is accomplished via direct methods of calculus of variation and the use of a Maz’ya type inequality, which is a consequence of the Poincaré inequality. However, when the domain and its boundary are unbounded, such a method is unavailable. In this paper, using the technique of sphericalization developed in the prior paper~[32], we establish the existence of solutions to the Dirichlet boundary value problem for $p$-harmonic functions in unbounded uniform domains with unbounded boundary when $1<p<\infty$. We also explore the issue of whether such solutions are unique by considering $p$-parabolicity and $p$-hyperbolicity properties of the domain.
4. 测度涡度的定量拟能界
Quantitative enstrophy bounds for measure vorticities
作者: Luigi De Rosa, Margherita Marcotullio
类别: math.AP, math-ph, physics.flu-dyn
发布日期: 2026-02-17
arXiv ID: 2602.15670v1
链接: http://arxiv.org/abs/2602.15670v1
摘要: We consider the two-dimensional incompressible Navier-Stokes equations with measure initial vorticity. By means of improved Nash inequalities, we establish quantitative estimates for the enstrophy depending on the absolute vorticity decay on balls. The bounds are optimal in several aspects and yield to a conjecturally sharp rate of the dissipation in the Delort’s class.
5. 关于多连通区域中拉普拉斯方程的罗宾问题
On the Robin problem for the Laplace equation in multiply connected domains
作者: Alberto Cialdea, Vita Leonessa
类别: math.AP
发布日期: 2026-02-17
arXiv ID: 2602.15647v1
链接: http://arxiv.org/abs/2602.15647v1
摘要: This paper complements the existing theory developed in [5] for the Dirichlet and Neumann problems for the Laplace equation, in multiply connected domains. Within the framework of layer potential methods, we study the Laplace equation under Robin boundary conditions, representing the solutions by means of a double layer potential. We observe that the classical approach searches the solutions in terms of a single layer potential.
6. 抛物型方程边界上的完备性定理
Completeness theorems on the boundary for a parabolic equation
作者: Alberto Cialdea, Carmine Sebastiano Mare
类别: math.AP
发布日期: 2026-02-17
arXiv ID: 2602.15621v1
链接: http://arxiv.org/abs/2602.15621v1
摘要: Let $\{v_α\}$ be a system of polynomial solutions of the parabolic equation $a_{hk}\partial_{x_{h}x_{k}}u - \partial_t u =0$ in a bounded $C^1$-cylinder $Ω_{T}$ contained in $\mathbb{R}^{n+1}$. Here $a_{hk}\partial_{x_{h}x_{k}}$ is an elliptic operator with real constant coefficients. We prove that $\{v_α\}$ is complete in $L^{p}(Σ')$, where $Σ'$ is the parabolic boundary of $Ω_{T}$. Similar results are proved for the adjoint equation $a_{hk}\partial_{x_{h}x_{k}} u+ \partial_t u =0$.
7. 非截断玻尔兹曼方程弱解的唯一性与零阶分析
Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation
作者: Dingqun Deng, Shota Sakamoto
类别: math.AP
发布日期: 2026-02-17
arXiv ID: 2602.15601v1
链接: http://arxiv.org/abs/2602.15601v1
摘要: We establish the uniqueness of large solutions to the non-cutoff Boltzmann equation with moderate soft potentials. Specifically, the weak solution $F=μ+μ^{\frac{1}{2}}f$ is unique as long as it has finite energy, in the sense that the norm $\|f\|_{L^\infty_t L^{r}_{x,v}}+\|f\|_{L^\infty_t L^2_{x,v}}$ remains bounded (arbitrary large) for some sufficiently large $r>0$. Our approach applies dilated dyadic decompositions in phase space $(v,ξ,η)$ to capture hypoellipticity and to reduce the fractional derivative structure $(-Δ_v)^{s}$ of the Boltzmann collision operator to zeroth order. The difficulties posed by the large solution are overcome through the negative-order hypoelliptic estimate that gains integrability in $(t,x)$.
8. 可通过输运求解的退化椭圆系统：一个警示性实例
A Degenerate Elliptic System Solvable by Transport: A Cautionary Example
作者: Daniel Alayón-Solarz
类别: math.AP, math.CV, math.NA
发布日期: 2026-02-17
arXiv ID: 2602.15479v1
链接: http://arxiv.org/abs/2602.15479v1
摘要: We exhibit a one-parameter family of first-order real elliptic systems on the plane whose ellipticity constant degenerates to zero as $δ\to 0$, with condition number $κ= O(δ^{-2})$. For any fixed elliptic solver operating at finite precision, the parameter $δ$ can be chosen small enough to defeat the solver; no uniform numerical scheme based on the ellipticity constant alone can handle the entire family. Despite this, every member of the family is explicitly solvable – and its initial value problem well posed – by elementary means once a transport-theoretic invariant is identified. The cost of the transport solution is independent of $δ$. The example serves as a cautionary tale: the ellipticity constant alone does not determine the practical difficulty of a first-order PDE. Before invoking an elliptic solver, one should compute the transport obstruction $G$; its vanishing – or smallness – signals structure that standard elliptic methods miss entirely.
9. 圆盘上具有给定负高斯曲率与边界测地曲率的共形度量
Conformal Metrics on the Disk with Prescribed Negative Gaussian Curvature and Boundary Geodesic Curvature
作者: Rafael López-Soriano, Francisco J. Reyes-Sánchez, David Ruiz
类别: math.AP, math.DG
发布日期: 2026-02-17
arXiv ID: 2602.15471v1
链接: http://arxiv.org/abs/2602.15471v1
摘要: We study the problem of prescribing the Gaussian curvature on the disk and the geodesic curvature on its boundary via a conformal change of the metric. In this paper the case of negative Gaussian curvature is treated, a regime for which the bubbling behavior of approximate solutions is not so well understood. This is due to the possible appearance of blow-up solutions with diverging length and area. We give an existence result under assumptions on the curvatures which are somewhat natural, in view of some obstructions inherent to the problem. Our strategy is variational and relies on the study of certain families of approximated problems. By performing a refined blow-up analysis for solutions with bounded Morse index, we conclude compactness.
10. 定常可压缩流中液 - 气相变的正则化框架与容许解
A Regularized Framework and Admissible Solutions for Liquid-Vapor Phase Transitions in Steady Compressible Flows
作者: Yazhou Chen, Qiaolin He, Dongjuan Niu, Yi Peng, Xiaoding Shi
类别: math.AP
发布日期: 2026-02-17
arXiv ID: 2602.15394v1
链接: http://arxiv.org/abs/2602.15394v1
摘要: We investigate the well-posedness of the periodic boundary value problem for the steady compressible isentropic Navier-Stokes system under the van der Waals equation of state. The main difficulty arises from the non-monotonicity of the pressure, which induces liquid-vapor phase transitions and consequently leads to both physical instabilities and mathematical non-uniqueness of solutions. It is shown that the occurrence of a phase transition is determined by whether the integral average of the specific volume lies inside the gas-liquid coexistence region defined by the Maxwell construction. By introducing an artificial viscosity, we construct an approximate system. When the integral average of the specific volume falls within the Maxwell region, the approximate solution converges, as the artificial viscosity tends to zero, to the equilibrium states given by Maxwell’s construction, with the diffuse interface sharpening into a discontinuity. Conversely, if the integral average of the specific volume lies outside this region, the limiting solution remains outside as well, meaning that no phase transition occurs. These results demonstrate that the non-monotonicity of the pressure, combined with the condition that the integral average of the specific volume belongs to the Maxwell region, can act as a nucleation mechanism for phase transitions in the isentropic gas-liquid problem. Furthermore, the proposed approximation not only offers a regularized framework for describing phase transitions but also provides, from a rigorous mathematical viewpoint, a definition of admissible solutions related to phase transitions. The detailed proof relies on the artificial viscosity method, the calculus of variations, the anti-derivative technique, phase-plane analysis, and the level-set method.
11. 具有傅里叶边界条件的热方程的卡尔曼不等式：在零能控性问题中的应用
Carleman Inequalities for the Heat Equation with Fourier Boundary Conditions: Applications to Null Controllability Problems
作者: Jose Antonio Villa
类别: math.OC, math.AP
发布日期: 2026-02-17
arXiv ID: 2602.15300v1
链接: http://arxiv.org/abs/2602.15300v1
摘要: In this work, we establish a Carleman inequality for the heat equation with Fourier boundary conditions of the form $\partial_νy+by=f1_γ$, where the control acts on a small portion $γ$ of the boundary. We apply this inequality to address the null controllability problem with boundary control supported on this small region. An explicit solution to this problem is obtained via a system of coupled parabolic equations. Based on these results, we propose an iterative numerical method to solve the coupled system.
12. 紧李群上一类演化算子的可解性
Solvability of a class of evolution operators on compact Lie groups
作者: Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro
类别: math.AP
发布日期: 2026-02-16
arXiv ID: 2602.15203v1
链接: http://arxiv.org/abs/2602.15203v1
摘要: This paper provides sufficient conditions for the solvability of a class of first-order evolution operators of Vekua-type on the product of a one-dimensional torus and a compact Lie group. The conditions are expressed in terms of the time-dependent coefficients and the spectral behavior of a normalized left-invariant vector field on the group. The three-sphere case is discussed in detail, leading to more explicit criteria, and the main results are further extended to operators defined on finite products of compact Lie groups.
13. 自相似欧拉方程的双汇解
A Two-Sink Solution to the Self-Similar Euler Equations
作者: Hyungjun Choi, Matei P. Coiculescu
类别: math.AP, physics.flu-dyn
发布日期: 2026-02-16
arXiv ID: 2602.15152v1
链接: http://arxiv.org/abs/2602.15152v1
摘要: We construct the first known example of a self-similar solution to the two-dimensional incompressible Euler equations whose pseudo-velocity has more than one stagnation point. The solution is also a homogeneous steady state of the Euler equations. In contrast, any homogeneous steady state with bounded vorticity necessarily admits only a single stagnation point at the origin. Our construction develops cusps in the velocity along two lines passing through the origin, thereby allowing stagnation points other than the origin.
14. 双曲 sinh-Gordon 模型的不变吉布斯动力学
Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model
作者: Justin Forlano, Younes Zine
类别: math.AP, math-ph, math.PR
发布日期: 2026-02-16
arXiv ID: 2602.14996v1
链接: http://arxiv.org/abs/2602.14996v1
摘要: We study the hyperbolic defocusing sinh-Gordon model with parameter $β^2>0$ and its associated Gibbs dynamics on the two-dimensional torus. We establish global well-posedness of the model for a certain range of parameters $β^2>0$ with the corresponding Gibbs measure initial data and prove invariance of the Gibbs measure under the flow, thereby resolving a question posed by Oh, Robert, and Wang (2019). Our physical space approach hinges on developing a novel $L^\infty$-based well-posedness theory for wave equations with exponential-type nonlinearities, going beyond the classical $L^2$-based framework. This refinement allows us to fully leverage structural properties of Gaussian multiplicative chaos. As a by-product of our method, we also obtain an improved well-posedness theory for the hyperbolic Liouville model.