Analysis of PDEs

Authors and titles for September 2024

[1] arXiv:2409.00073 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Dynamics of threshold solutions for the energy-critical inhomogeneous NLS Show Chinese title

Title: 阈值解的动力学对于能量临界非均匀NLS

Xuan Liu, Kai Yang, Ting Zhang

Subjects: Analysis of PDEs (math.AP)

[2] arXiv:2409.00076 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: A dispersive effective equation for transverse propagation of planar shallow water waves over periodic bathymetry Show Chinese title

Title: 横向上平面浅水波在周期性地形上的传播的色散有效方程

David I. Ketcheson, Giovanni Russo

Journal-ref: J. nonlinear waves 1 (2025) e1

Subjects: Analysis of PDEs (math.AP) ; Dynamical Systems (math.DS) ; Fluid Dynamics (physics.flu-dyn)

[3] arXiv:2409.00117 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Pointwise estimates for the fundamental solutions of higher order Schrödinger equations in odd dimensions II: high dimensional case Show Chinese title

Title: 高维情形下奇数维更高阶薛定谔方程基本解的逐点估计 II：高维情况

Han Cheng, Shanlin Huang, Tianxiao Huang, Quan Zheng

Comments: typos cerrected

Subjects: Analysis of PDEs (math.AP)

[4] arXiv:2409.00136 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations Show Chinese title

Title: 非阿基米德伪微分方程新类的基本解

Anatoly N. Kochubei, Mariia V. Serdiuk

Subjects: Analysis of PDEs (math.AP)

[5] arXiv:2409.00152 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: A strongly degenerate fully nonlinear mean field game with nonlocal diffusion Show Chinese title

Title: 具有非局部扩散的强退化完全非线性平均场游戏

Indranil Chowdhury, Espen R. Jakobsen, Miłosz Krupski

Comments: Earlier version of arXiv:2104.06985 has been split into two articles. The latest version of arXiv:2104.06985 is now the first part and this article is the second part

Subjects: Analysis of PDEs (math.AP)

[6] arXiv:2409.00307 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Boundary driven instabilities of Couette flows Show Chinese title

Title: 剪切流的边界驱动不稳定性

Dongfen Bian, Emmanuel Grenier, Nader Masmoudi, Weiren Zhao

Subjects: Analysis of PDEs (math.AP)

[7] arXiv:2409.00311 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: The 3D kinetic Couette flow via the Boltzmann equation in the diffusive limit Show Chinese title

Title: 三维扩散极限下通过玻尔兹曼方程的柯埃特流动

Renjun Duan, Shuangqian Liu, Robert M. Strain, Anita Yang

Subjects: Analysis of PDEs (math.AP)

[8] arXiv:2409.00365 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Singular semilinear elliptic equations in half-spaces Show Chinese title

Title: 半空间中的奇异半线性椭圆方程

Phuong Le

Comments: 19 pages

Subjects: Analysis of PDEs (math.AP)

[9] arXiv:2409.00382 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Bifurcation diagrams for semilinear elliptic equations with singular weights in two dimensions Show Chinese title

Title: 二维带有奇异权的半线性椭圆方程的分岔图

Kenta Kumagai

Comments: 24 pages

Subjects: Analysis of PDEs (math.AP)

[10] arXiv:2409.00386 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Free boundary value problem for the radial symmetric compressible isentropic Navier-Stokes equations with density-dependent viscosity Show Chinese title

Title: 密度依赖粘性径向对称可压缩等熵纳维-斯托克斯方程的自由边界值问题

Xiangdi Huang, Weili Meng, Anchun Ni

Comments: 27pages

Subjects: Analysis of PDEs (math.AP)

[11] arXiv:2409.00439 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: An abstract generalization of Källen-Kröner's interation Show Chinese title

Title: Källen-Kröner相互作用的抽象推广

Ángel D. Martínez

Comments: This has been published as an Appendix to another paper, namely Trans. Amer. Math. Soc. 377 (2024), pp. 5411-5444

Subjects: Analysis of PDEs (math.AP)

[12] arXiv:2409.00446 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Nonlinear two-dimensional water waves with arbitrary vorticity Show Chinese title

Title: 非线性二维水波与任意涡度

Delia Ionescu-Kruse, Rossen Ivanov

Comments: 36 pages, 4 figures

Journal-ref: Journal of Differential Equations 368 (2023), Pages 317-349

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph) ; Pattern Formation and Solitons (nlin.PS)

[13] arXiv:2409.00467 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Well-posedness for a higher order water wave model on modulation spaces Show Chinese title

Title: 高阶水波模型在调制空间上的适定性

Xavier Carvajal, Mahendra Panthee

Comments: 35 pages

Subjects: Analysis of PDEs (math.AP)

[14] arXiv:2409.00482 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Singular Elliptic PDEs: an extensive overview Show Chinese title

Title: 奇异椭圆PDEs：全面概述

Francescantonio Oliva, Francesco Petitta

Journal-ref: Partial Differential Equations and Applications, 2025

Subjects: Analysis of PDEs (math.AP)

[15] arXiv:2409.00519 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Blow-up solutions for the steady state of the Keller-Segel system on Riemann surfaces Show Chinese title

Title: Keller-Segel系统在黎曼曲面上的稳态爆破解

Mohameden Ahmedou, Thomas Bartsch, Zhengni Hu

Subjects: Analysis of PDEs (math.AP)

[16] arXiv:2409.00528 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Existence and weak-strong uniqueness for damage systems in viscoelasticity Show Chinese title

Title: 粘弹性中的损伤系统的存在性及弱强唯一性

Robert Lasarzik, Elisabetta Rocca, Riccarda Rossi

Subjects: Analysis of PDEs (math.AP)

[17] arXiv:2409.00537 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On the uniqueness of the optimal control for 2-dimensional second grade fluids Show Chinese title

Title: 二维二阶流体最优控制的唯一性

Adilson Almeida, Nikolai V. Chemetov, Fernanda Cipriano

Journal-ref: Electron. J. Differential Equations, Vol. 2022 (2022), No. 22, pp. 1-12

Subjects: Analysis of PDEs (math.AP) ; Optimization and Control (math.OC)

[18] arXiv:2409.00579 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Data Assimilation to the Primitive Equations in $H^2$ Show Chinese title

Title: 数据同化到原始方程在$H^2$

Ken Furukawa

Subjects: Analysis of PDEs (math.AP) ; Dynamical Systems (math.DS)

[19] arXiv:2409.00619 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On an Inverse Problem of the Generalized Bathtub Model of Network Trip Flows Show Chinese title

Title: 关于广义浴缸模型网络行程流的逆问题

Kuang Huang, Bangti Jin, Zhi Zhou

Comments: 25 pages, 3 figures

Subjects: Analysis of PDEs (math.AP) ; Numerical Analysis (math.NA)

[20] arXiv:2409.00646 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Liouville Theorem for Lane-Emden Equation on the Heisenberg Group Show Chinese title

Title: 关于Heisenberg群上Lane-Emden方程的Liouville定理

Hua Chen, Xin Liao

Comments: There is an error in equation 2.14. For equation 2.14 to hold, the function $u$ should be cylindrical

Subjects: Analysis of PDEs (math.AP)

[21] arXiv:2409.00725 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Smooth compactness of elasticae Show Chinese title

Title: 弹性曲线的光滑紧性

Tatsuya Miura

Comments: 14 pages, 3 figures, proof of Theorem 3.7 fixed

Subjects: Analysis of PDEs (math.AP) ; Differential Geometry (math.DG)

[22] arXiv:2409.00820 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Allard-type regularity theory for area minimizing currents at boundaries with arbitrary multiplicity Show Chinese title

Title: 边界上任意重数的面积最小电流的Allard型正则性理论

Ian Fleschler

Comments: To appear in the proceedings of the conference "Geometric Measure Theory and Applications", held in Cortona, 2024. The proceedings will be published in the Springer INdAM Series

Subjects: Analysis of PDEs (math.AP) ; Differential Geometry (math.DG)

[23] arXiv:2409.00902 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Inverse coefficient problems for one-dimensional time-fractional diffusion equations Show Chinese title

Title: 一维时间分数阶扩散方程的逆系数问题

Oleg Imanuvilov, Kazufumi Ito, Masahiro Yamamoto

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph)

[24] arXiv:2409.00939 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Far Field Asymptotics of Nematic Flows Around a Small Spherical Particle Show Chinese title

Title: 向心流在小球形粒子周围的远场渐近行为

Dmitry Golovaty, Nung Kwan Yip

Subjects: Analysis of PDEs (math.AP) ; Soft Condensed Matter (cond-mat.soft)

[25] arXiv:2409.00961 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Variational construction of singular characteristics and propagation of singularities Show Chinese title

Title: 变分构造奇异特征和奇异性的传播

Piermarco Cannarsa, Wei Cheng, Jiahui Hong, Kaizhi Wang

Subjects: Analysis of PDEs (math.AP) ; Dynamical Systems (math.DS)

[26] arXiv:2409.00976 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On De Giorgi's lemma for variational interpolants in metric and Banach spaces Show Chinese title

Title: 关于度量和巴拿赫空间中变分插值的德·乔治引理

Alexander Mielke, Riccarda Rossi

Subjects: Analysis of PDEs (math.AP)

[27] arXiv:2409.00990 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Optimal regularity of subsonic steady-states solution of Euler-Poisson equations for semiconductors with sonic boundary Show Chinese title

Title: 欧拉-泊松方程在声学边界条件下半导体亚音速稳态解的最优正则性

Siying Li, Ming Mei, Kaijun Zhang, Guojing Zhang

Subjects: Analysis of PDEs (math.AP)

[28] arXiv:2409.01031 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On the well-posedness of the compressible Navier-Stokes equations Show Chinese title

Title: 关于可压缩纳维-斯托克斯方程的适定性

Zihua Guo, Minghua Yang, Zeng Zhang

Subjects: Analysis of PDEs (math.AP)

[29] arXiv:2409.01045 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: A charged liquid drop model with Willmore energy Show Chinese title

Title: 带电液滴模型与威洛比能量

Michael Goldman, Matteo Novaga, Berardo Ruffini

Subjects: Analysis of PDEs (math.AP)

[30] arXiv:2409.01047 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: A microscopic derivation of a traffic flow model on a junction with two entry lines Show Chinese title

Title: 一个具有两条入口线的交叉口交通流模型的微观推导

P Cardaliaguet (CEREMADE)

Subjects: Analysis of PDEs (math.AP)

[31] arXiv:2409.01067 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Well-posedness, long-time behavior, and discretization of some models of nonlinear acoustics in velocity-enthalpy formulation Show Chinese title

Title: 适定性、长时间行为及速度-焓公式中一些非线性声学模型的离散化

Herbert Egger, Marvin Fritz

Subjects: Analysis of PDEs (math.AP) ; Numerical Analysis (math.NA)

[32] arXiv:2409.01096 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Carleson measures on domains in Heisenberg groups Show Chinese title

Title: 赫尔曼群中的Carleson测度

Tomasz Adamowicz, Marcin Gryszówka

Comments: 28 pg

Subjects: Analysis of PDEs (math.AP) ; Complex Variables (math.CV)

[33] arXiv:2409.01134 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: The Klein-Gordon equation on asymptotically Minkowski spacetimes: causal propagators Show Chinese title

Title: 渐近闵可夫斯基时空上的克莱因-戈登方程：因果传播子

Dean Baskin, Moritz Doll, Jesse Gell-Redman

Comments: 94 pages, 6 figures

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph)

[34] arXiv:2409.01142 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Nonlinear stability threshold for compressible Couette flow Show Chinese title

Title: 可压缩库埃特流的非线性稳定性阈值

Feimin Huang, Rui Li, Lingda Xu

Comments: 45 pages, all comments are welcome

Subjects: Analysis of PDEs (math.AP)

[35] arXiv:2409.01182 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Overhanging solitary water waves Show Chinese title

Title: 悬垂孤立水波

Juan Dávila, Manuel del Pino, Monica Musso, Miles H. Wheeler

Comments: 93 pages

Subjects: Analysis of PDEs (math.AP)

[36] arXiv:2409.01183 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On the monotonicity of the Fisher information for the Boltzmann equation Show Chinese title

Title: 关于玻尔兹曼方程的费舍尔信息的单调性

Cyril Imbert, Luis Silvestre, Cédric Villani

Comments: 35 pages

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph)

[37] arXiv:2409.01196 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Charge transport systems with Fermi-Dirac statistics for memristors Show Chinese title

Title: 具有费米-狄拉克统计的忆阻器电荷传输系统

Maxime Herda, Ansgar Jüngel, Stefan Portisch

Comments: Correction of the proof of Lemma 16

Subjects: Analysis of PDEs (math.AP)

[38] arXiv:2409.01229 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Thermo-elastodynamics of nonlinearly viscous solids Show Chinese title

Title: 非线性粘性固体的热弹性动力学

S. Almi, R. Badal, M. Friedrich, S. Schwarzacher

Subjects: Analysis of PDEs (math.AP)

[39] arXiv:2409.01349 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: A weighted eigenvalue problem for mixed local and nonlocal operators with potential Show Chinese title

Title: 带有势的混合局部和非局部算子的加权特征值问题

R. Lakshmi, Ratan Kr. Giri, Sekhar Ghosh

Comments: 28 pages

Subjects: Analysis of PDEs (math.AP)

[40] arXiv:2409.01474 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Homogenization of the 2D Euler system: lakes and porous media Show Chinese title

Title: 二维欧拉系统的均质化：湖泊和多孔介质

Mitia Duerinckx, Antoine Gloria

Comments: 32 pages

Subjects: Analysis of PDEs (math.AP)

[41] arXiv:2409.01494 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Three dimensional stationary solutions of the Electron MHD equations Show Chinese title

Title: 三维稳态解的电子MHD方程

Qirui Peng

Comments: Several typos fixed

Subjects: Analysis of PDEs (math.AP)

[42] arXiv:2409.01505 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: The Cauchy problem for the Degasperis-Procesi Equation: Painlevé Asymptotics in Transition Zones Show Chinese title

Title: Degasperis-Procesi方程的柯西问题：过渡区域中的Painlevé渐近行为

Zhaoyu Wang, Xuan Zhou, Engui Fan

Comments: 48 pages

Subjects: Analysis of PDEs (math.AP)

[43] arXiv:2409.01507 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation Show Chinese title

Title: Rayleigh-Jeans平衡在动能FPU方程中的稳定性

Pierre Germain, Joonhyun La, Angeliki Menegaki

Comments: 34 pages

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph)

[44] arXiv:2409.01583 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: On the anisotropic Calderón's problem Show Chinese title

Title: 关于各向异性Calderón问题

Gunther Uhlmann, Jian Zhai

Comments: The argument is incorrect

Subjects: Analysis of PDEs (math.AP) ; Differential Geometry (math.DG)

[45] arXiv:2409.01640 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Two-layers neural networks for Schr{ö}dinger eigenvalue problems Show Chinese title

Title: Two-layers neural networks for Schr{ö}dinger eigenvalue problems

Mathias Dus (ENPC), Ehrlacher Virginie (ENPC)

Subjects: Analysis of PDEs (math.AP) ; Optimization and Control (math.OC) ; Probability (math.PR)

[46] arXiv:2409.01663 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Small-amplitude finite-depth Stokes waves are transversally unstable Show Chinese title

Title: 小振幅有限深度斯托克斯波是横向不稳定的

Ziang Jiao, L. Miguel Rodrigues, Changzhen Sun, Zhao Yang

Comments: Slighted extended revised version, 32 pages, 2 figures

Subjects: Analysis of PDEs (math.AP)

[47] arXiv:2409.01703 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Piecewise regular solutions to scalar balance laws with singular nonlocal sources Show Chinese title

Title: 标量平衡律的分段正则解与奇异非局部源

Lorena Bociu, Evangelia Ftaka, Khai T. Nguyen, Jacopo Schino

Journal-ref: J. Differential Equations 409 (2024), 181--222

Subjects: Analysis of PDEs (math.AP)

[48] arXiv:2409.01748 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Stability of the Von Kármán regime for thin plates under Neumann boundary conditions Show Chinese title

Title: 在Neumann边界条件下的薄板Von Kármán区域的稳定性

Edoardo Giovanni Tolotti

Comments: Post peer-review version

Journal-ref: ESAIM: Control, Optimisation and Calculus of Variations 31, 61 (2025)

Subjects: Analysis of PDEs (math.AP)

[49] arXiv:2409.01774 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Boundary regularity for the distance functions, and the eikonal equation Show Chinese title

Title: 距离函数的边界正则性与几何光学方程

Nikolai Nikolov, Pascal J. Thomas

Comments: version 2; to appear in Journal of Geometric Analysis

Subjects: Analysis of PDEs (math.AP) ; Complex Variables (math.CV)

[50] arXiv:2409.01811 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: A constitutive condition for idealized isotropic Cauchy elasticity involving the logarithmic strain Show Chinese title

Title: 理想各向同性柯西弹性涉及对数应变的本构条件

Marco Valerio d'Agostino, Sebastian Holthausen, Davide Bernardini, Adam Sky, Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph)