Analysis of PDEs

Authors and titles for October 2023

[1] arXiv:2310.00025 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: The extension problem for fractional powers of higher order of some evolutive operators Show Chinese title

Title: 某些演化算子的分数阶幂的延拓问题

Pietro Gallato

Comments: Thesis defended on October 5th, 2022. The results were presented in the minicourse "Fractional calculus and heat equation: from the classics to present time", taught by N. Garofalo in Sept 2022 at the Mittag-Leffler Institute. The video of the mini course is available at the web site https://www.mittag-leffler.se/activities/geometric-aspects-of-nonlinear-partial-differential-equations/

Subjects: Analysis of PDEs (math.AP)

[2] arXiv:2310.00209 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Nonlinear stability of entropy waves for the Euler equations Show Chinese title

Title: 欧拉方程的熵波非线性稳定性

Wei Wang, Zhifei Zhang, Wenbin Zhao

Comments: 23 pages. One appendix deleted. All comments are welcome

Subjects: Analysis of PDEs (math.AP)

[3] arXiv:2310.00217 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Regularity criteria of 3D generalized magneto-micropolar fluid system in terms of the pressure Show Chinese title

Title: 关于3D广义磁微极流体系统压力的正则性准则

Jae-Myoung Kim

Subjects: Analysis of PDEs (math.AP)

[4] arXiv:2310.00269 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Well-posedness and Long Time Behavior of the Euler Alignment System with Adaptive Communication Strength Show Chinese title

Title: 适定性与自适应通信强度下欧拉对齐系统的长期行为

Roman Shvydkoy, Trevor Teolis

Subjects: Analysis of PDEs (math.AP)

[5] arXiv:2310.00537 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: On the Existence of Solution of Conservation Law with Moving Bottleneck and Discontinuity in FLux Show Chinese title

Title: 关于具有移动瓶颈和通量不连续性的守恒律解的存在性

Hossein Nick Zinat Matin, Maria Laura Delle Monache

Comments: 51 pages, 29 Figures

Subjects: Analysis of PDEs (math.AP)

[6] arXiv:2310.00556 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Axial Symmetry of Normalized Solutions for Magnetic Gross-Pitaevskii Equations with Anharmonic Potentials Show Chinese title

Title: 磁势非谐势下归一化解的轴对称性

Yujin Guo, Yan Li, Yong Luo, Shuangjie Peng

Subjects: Analysis of PDEs (math.AP)

[7] arXiv:2310.00628 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Low Mach number limit of strong solutions to the compressible primitive equations with gravity Show Chinese title

Title: 可压缩原始方程组在重力作用下强解的低马赫数极限

Pengcheng Mu

Subjects: Analysis of PDEs (math.AP)

[8] arXiv:2310.00645 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: An alternative proof of the $L^p$-regularity problem for Dahlberg-Kenig-Pipher operators on $\mathbb R^n_+$ Show Chinese title

Title: Dahlberg-Kenig-Pipher 算子在$\mathbb R^n_+$上的$L^p$-正则性问题的另一种证明

Joseph Feneuil

Comments: 22 pages

Subjects: Analysis of PDEs (math.AP)

[9] arXiv:2310.00700 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Carleman Estimates for Second Order Elliptic Operators with Limiting Weights, an Elementary Approach Show Chinese title

Title: Carleman 估计用于带有极限权重的二阶椭圆算子，一种简单的方法

Zengyu Li, Qi Lü

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

[10] arXiv:2310.00732 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Leapfrogging vortex rings as scaling limit of Euler Equations Show Chinese title

Title: 跳跃涡环作为欧拉方程的标度极限

Paolo Buttà, Guido Cavallaro, Carlo Marchioro

Comments: 33 pages, 1 figure; typos corrected, references updated

Journal-ref: SIAM J. Math. Anal. 57 (2025), pp. 789-824

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

[11] arXiv:2310.00756 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Stability and bifurcation for logistic Keller--Segel models on compact graphs Show Chinese title

Title: 稳定性与分支对于紧致图上的逻辑斯蒂Keller--Segel模型

Hewan Shemtaga, Wenxian Shen, Selim Sukhtaiev

Subjects: Analysis of PDEs (math.AP) ; Spectral Theory (math.SP)

[12] arXiv:2310.00767 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Sobolev spaces for singular perturbation of Laplace operato Show Chinese title

Title: Sobolev空间用于Laplace算子的奇异摄动

Vladimir Georgiev, Mario Rastrelli

Comments: 20 pages

Subjects: Analysis of PDEs (math.AP) ; Functional Analysis (math.FA)

[13] arXiv:2310.00777 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Local well-posedness of the Vlasov-Poisson-Landau system and related models Show Chinese title

Title: Vlasov-Poisson-Landau系统的局部适定性及相关模型

Patrick Flynn

Comments: 26 pages

Journal-ref: Kinetic and Related Models (2024): 0-0

Subjects: Analysis of PDEs (math.AP)

[14] arXiv:2310.00869 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: The regularity of the coupled system between an electrical network with fractional dissipation and a plate equation with fractional inertial rotational Show Chinese title

Title: 具有分数阻尼的电气网络与具有分数惯性旋转的板方程之间的耦合系统的正则性

Santos R.W.S. Bejarano, Filomena B.R. Mendes, Fredy M. Sobrado Suárez, Gilson Tumelero, Marieli M. Tumelero

Comments: 40 pages

Subjects: Analysis of PDEs (math.AP)

[15] arXiv:2310.00925 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications Show Chinese title

Title: 非局部Hamilton-Jacobi方程粘性解的表示公式及其应用

Takashi Kagaya, Qing Liu, Hiroyoshi Mitake

Comments: 33 pages

Subjects: Analysis of PDEs (math.AP)

[16] arXiv:2310.00979 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Gevrey WKB method for PDO's of real principal type Show Chinese title

Title: 实主型PDO的Gevrey WKB方法

Richard Lascar, Ivan Moyano

Subjects: Analysis of PDEs (math.AP)

[17] arXiv:2310.00988 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Stability and Optimal Decay Rates for Abstract Systems with Thermal Damping of Cattaneo's Type Show Chinese title

Title: 稳定性与具有Cattaneo型热阻尼的抽象系统的最优衰减率

Chenxi Deng, Zhong-Jie Han, Zhaobin Kuang, Qiong Zhang

Comments: typos corrected

Subjects: Analysis of PDEs (math.AP)

[18] arXiv:2310.00992 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Logarithmic Sobolev, Hardy and Poincaré inequalities on the Heisenberg group Show Chinese title

Title: 对Heisenberg群上的对数Sobolev、Hardy和Poincaré不等式

Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky

Comments: 41 pages

Subjects: Analysis of PDEs (math.AP) ; Functional Analysis (math.FA) ; Group Theory (math.GR)

[19] arXiv:2310.01017 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: A Stochastic Porous Media Schr{ö}dinger Equation: Feynman-type Motivation, Well-Posedness and Control Interpretation Show Chinese title

Title: A Stochastic Porous Media Schr{ö}dinger Equation: Feynman-type Motivation, Well-Posedness and Control Interpretation

Ioana Ciotir (LMI), Dan Goreac (LAMA), Juan Li, Xinru Zhang

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph) ; Optimization and Control (math.OC)

[20] arXiv:2310.01019 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes Show Chinese title

Title: 一维近三次非线性薛定谔方程孤立波在无内部模态情况下的渐近稳定性

Guillaume Rialland

Subjects: Analysis of PDEs (math.AP)

[21] arXiv:2310.01048 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Gaussian estimates for general parabolic operators in dimension 1 Show Chinese title

Title: 一维中一般抛物型算子的高斯估计

Grégoire Nadin (IDP, CNRS)

Subjects: Analysis of PDEs (math.AP)

[22] arXiv:2310.01054 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Lattice tilings minimizing nonlocal perimeters Show Chinese title

Title: 格子铺砌最小化非局部周长

Annalisa Cesaroni, Ilaria Fragalà, Matteo Novaga

Comments: 19 pages, 2 figures

Subjects: Analysis of PDEs (math.AP)

[23] arXiv:2310.01085 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Canonical solutions to non-translation invariant singular SPDEs Show Chinese title

Title: 非平移不变奇异SPDE的经典解

Harprit Singh

Comments: Accepted version

Subjects: Analysis of PDEs (math.AP) ; Probability (math.PR)

[24] arXiv:2310.01172 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Stability conditions for mean-field limiting vorticities of the Ginzburg-Landau equations in 2D Show Chinese title

Title: 二维Ginzburg-Landau方程平均场极限涡量的稳定性条件

Rémy Rodiac

Comments: 29 pages

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

[25] arXiv:2310.01175 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Homogenization of supremal functionals in the vectorial case (via $L^p$-approximation) Show Chinese title

Title: 向量情形下上确界泛函的均质化（通过$L^p$-逼近）

Lorenza D'Elia, Michela Eleuteri, Elvira Zappale

Subjects: Analysis of PDEs (math.AP)

[26] arXiv:2310.01192 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Eigenvalues and resonances of dissipative acoustic operator for strictly convex obstacles Show Chinese title

Title: 特征值和耗散声学算子的共振对于严格凸障碍物

Vesselin Petkov

Comments: This is a revised version of the paper with some new details of the exposition and corrections of misprints

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

[27] arXiv:2310.01193 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: The primitive equations with rough transport noise: Global well-posedness and regularity Show Chinese title

Title: 带有粗糙输运噪声的原始方程：全局适定性与正则性

Antonio Agresti

Comments: 67 pages, typos corrected

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

[28] arXiv:2310.01214 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems Show Chinese title

Title: 最小能量解的唯一性和非退化性到分数狄利克雷问题

Abdelrazek Dieb, Isabella Ianni, Alberto Saldaña

Comments: 25 pages. In this revised version, we have improved our symmetry result Theorem 1.2, which now holds for general non-negative solutions. Due to a mistake found in our previous version (see Remark 3.6), Theorem 1.1 is now stated only for large balls

Subjects: Analysis of PDEs (math.AP)

[29] arXiv:2310.01221 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Maximum principle preserving nonlocal diffusion model with Dirichlet boundary condition Show Chinese title

Title: 最大值原理保持的具有狄利克雷边界条件的非局部扩散模型

Yanzun Meng, Zuoqiang Shi

Comments: 36 pages, 1 figure

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

[30] arXiv:2310.01256 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs Show Chinese title

Title: 具有应用的Gevrey类隐映射定理及其在半线性椭圆PDE不确定性量化中的应用

Helmut Harbrecht, Marc Schmidlin, Christoph Schwab

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

[31] arXiv:2310.01328 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Improved regularity for the stochastic fast diffusion equation Show Chinese title

Title: 随机快速扩散方程的改进正则性

Ioana Ciotir, Dan Goreac, Jonas M. Tölle

Comments: 7 pages, 29 references

Journal-ref: Electronic Communications in Probability 29 (2024), no. 5, 1--7

Subjects: Analysis of PDEs (math.AP) ; Probability (math.PR)

[32] arXiv:2310.01340 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Extensions of Schoen--Simon--Yau and Schoen--Simon theorems via iteration à la De Giorgi Show Chinese title

Title: Schoen--Simon--Yau 和 Schoen--Simon 定理的迭代方法扩展，类似于 De Giorgi 的方法

Costante Bellettini

Comments: 34 pp

Journal-ref: Inventiones Mathematicae vol. 240, n. 1 (2025)

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

[33] arXiv:2310.01346 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: The $σ_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k<\frac{n}{2}$ Show Chinese title

Title: Riemannian流形上的$σ_k$-Loewner-Nirenberg问题对于$k<\frac{n}{2}$

Jonah A. J. Duncan, Luc Nguyen

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

[34] arXiv:2310.01359 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On a class of anisotropic Muckenhoupt weights and their applications to $p$-Laplace equations Show Chinese title

Title: 关于一类各向异性Muckenhoupt权及其在$p$-拉普拉斯方程中的应用

Changxing Miao, Zhiwen Zhao

Subjects: Analysis of PDEs (math.AP)

[35] arXiv:2310.01375 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Scaling laws and exact results in turbulence Show Chinese title

Title: 湍流中的标度定律和精确结果

Matthew Novack

Comments: 15 pages, no figures

Subjects: Analysis of PDEs (math.AP)

[36] arXiv:2310.01622 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: A critical neumann problem with anisotropic p-laplacian Show Chinese title

Title: 具有各向异性p-拉普拉斯算子的临界诺伊曼问题

Gustavo F. Madeira, Olímpio H. Miyakaki, Alânnio B. Nóbrega

Subjects: Analysis of PDEs (math.AP)

[37] arXiv:2310.01638 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on $\mathbb{T}$ Show Chinese title

Title: 关于格点、短时间估计和五次NLS在$\mathbb{T}$上的整体适定性

Ryan McConnell

Comments: 38 pages. Minor corrections

Subjects: Analysis of PDEs (math.AP)

[38] arXiv:2310.02026 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On Harnack inequality to the homogeneous nonlinear degenerate parabolic equations Show Chinese title

Title: 关于齐次非线性退化抛物方程的哈纳克不等式

Jasarat Gasimov, Farman Mamedov

Subjects: Analysis of PDEs (math.AP)

[39] arXiv:2310.02068 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Well-posedness and numerical analysis of an elapsed time model with strongly coupled neural networks Show Chinese title

Title: 适定性与强耦合神经网络的经过时间模型的数值分析

Mauricio Sepulveda, Nicolas Torres, Luis Miguel Villada

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

[40] arXiv:2310.02089 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On the number and geometric location of critical points of solutions to a semilinear elliptic equation in annular domains Show Chinese title

Title: 关于环形区域中半线性椭圆方程解的临界点的数量和几何位置

Haiyun Deng, Hairong Liu, Xiaoping Yang

Comments: 25 pages, 12 figures

Subjects: Analysis of PDEs (math.AP)

[41] arXiv:2310.02228 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Uniqueness of least energy solutions to the fractional Lane-Emden equation in the ball Show Chinese title

Title: 在球体中的分数Lane-Emden方程的最小能量解的唯一性

Azahara DelaTorre, Enea Parini

Comments: We corrected some minor issues of the previous version. The statement of the main theorem has been modified

Subjects: Analysis of PDEs (math.AP)

[42] arXiv:2310.02337 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Hilbert Expansion of Boltzmann Equation with Soft Potentials and Specular Boundary Condition in Half-space Show Chinese title

Title: Boltzmann方程在半空间中具有软势能和镜面边界条件的Hilbert展开

Jing Ouyang, Yong Wang

Comments: 40 pages, comments are welcome

Subjects: Analysis of PDEs (math.AP)

[43] arXiv:2310.02370 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Biological Aggregations from Spatial Memory and Nonlocal Advection Show Chinese title

Title: 从空间记忆和非局部对流产生的生物聚集

Di Liu, Yurij Salmaniw, Jonathan R. Potts, Junping Shi, Hao Wang

Comments: 33 pages, 9 figures

Subjects: Analysis of PDEs (math.AP) ; Spectral Theory (math.SP)

[44] arXiv:2310.02481 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: The fractional logarithmic Schrödinger operator: properties and functional spaces Show Chinese title

Title: 分数对数薛定谔算子：性质和函数空间

Pierre Aime Feulefack

Comments: 33 pages

Subjects: Analysis of PDEs (math.AP)

[45] arXiv:2310.02628 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: An existence theory for nonlinear superposition operators of mixed fractional order Show Chinese title

Title: 混合分数阶非线性超位置算子的存在性理论

Serena Dipierro, Kanishka Perera, Caterina Sportelli, Enrico Valdinoci

Subjects: Analysis of PDEs (math.AP)

[46] arXiv:2310.02652 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Ergodic Problems for Second-Order Mean Field Games with State Constraints Show Chinese title

Title: 具有状态约束的二阶平均场博弈的遍历问题

Alessio Porretta, Michele Ricciardi

Comments: 25 pages

Subjects: Analysis of PDEs (math.AP)

[47] arXiv:2310.02787 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Entire Monge-Ampère equations and weighted Minkowski problems Show Chinese title

Title: 整个Monge-Ampère方程和加权Minkowski问题

Jacopo Ulivelli

Subjects: Analysis of PDEs (math.AP) ; Metric Geometry (math.MG)

[48] arXiv:2310.02890 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Singularities of the network flow with symmetric initial data Show Chinese title

Title: 网络流的奇点与对称初始数据

Matteo Novaga, Luciano Sciaraffia

Comments: 10 pages, 2 figures

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

[49] arXiv:2310.02891 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Large-time behavior of two families of operators related to the fractional Laplacian on certain Riemannian manifolds Show Chinese title

Title: 两个与分数拉普拉斯相关的算子族在某些黎曼流形上的长时间行为

Effie Papageorgiou

Subjects: Analysis of PDEs (math.AP)

[50] arXiv:2310.02934 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Anomalous dissipation and Euler flows Show Chinese title

Title: 异常耗散和欧拉流

Jan Burczak, László Székelyhidi Jr., Bian Wu

Comments: Updated version 66 pages. The new version includes an extended introduction discussing implications for and the relationship to hydrodynamic turbulence, and a more general statement of the main result. Some minor typos were also corrected

Subjects: Analysis of PDEs (math.AP)