arXiv - MATH - Analysis of PDEs最新文献_第10页

On the Sobolev stability threshold for 3D Navier-Stokes equations with rotation near the Couette flow 论库特流附近旋转三维纳维-斯托克斯方程的索波列夫稳定性阈值

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI: arxiv-2409.05104

Wenting Huang, Ying Sun, Xiaojing Xu

{"title":"On the Sobolev stability threshold for 3D Navier-Stokes equations with rotation near the Couette flow","authors":"Wenting Huang, Ying Sun, Xiaojing Xu","doi":"arxiv-2409.05104","DOIUrl":"https://doi.org/arxiv-2409.05104","url":null,"abstract":"Rotation is one of the most important features of fluid flow in the\u0000atmosphere and oceans, which appears in almost all meteorological and\u0000geophysical models. When the speed of rotation is sufficiently large, the\u0000global existence of strong solution to the 3D Navier-Stokes equations with\u0000rotation has been obtained by the dispersion effect coming from Coriolis force\u0000(i.e., rotation). In this paper, we study the dynamic stability of the\u0000periodic, plane Couette flow in the three-dimensional Navier-Stokes equations\u0000with rotation at high Reynolds number $mathbf{Re}$. Our goal is to find the\u0000index of the stability threshold on $mathbf{Re}$: the maximum range of\u0000perturbations in which the solution to the equations remains stable. We first\u0000study the linear stability effects of linearized perturbed system. Compared\u0000with the results of Bedrossian, Germain and Masmoudi [Ann. of Math. 185(2):\u0000541--608 (2017)], mixing effects (which corresponds to enhanced dissipation and\u0000inviscid damping) arise from the Couette flow, Coriolis force acts as a\u0000restoring force which induces the dispersion mechanism of inertial waves and\u0000cancels the lift-up effect occurred in the zero frequency velocity. This\u0000dispersion mechanism bring good algebraic decay properties, which is different\u0000from the 3D classical Navier-Stokes equations. Therefore, we prove that the\u0000initial data satisfies $left|u_{mathrm{in}}right|_{H^{sigma}}<delta\u0000mathbf{Re}^{-1}$ for any $sigma>frac{9}{2}$ and some\u0000$delta=delta(sigma)>0$ depending only on $sigma$, the resulting solution to\u0000the 3D Navier-Stokes equations with rotation is global in time and does not\u0000transition away from the Couette flow. In the sense, Coriolis force is a factor\u0000that contributes to the stability of the fluid, which improves the stability\u0000threshold from $frac{3}{2}$ to $1$.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime 本征弱扩散体系中的空间非均质弗拉索夫-诺德斯特伦-福克-普朗克系统

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI: arxiv-2409.04966

Shengchuang Chang, Shuangqian Liu, Tong Yang

引用次数: 0

A short proof of the $mathcal C^{1,1}$ regularity for the eikonal equation 艾柯纳方程的 $mathcal C^{1,1}$ 正则性的简短证明

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI: arxiv-2409.05204

Radu Ignat

引用次数: 0

Concentration behavior of normalized ground states for mass critical Kirchhoff equations in bounded domains 有界域中质量临界基尔霍夫方程归一化基态的集中行为

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI: arxiv-2409.05130

Shubin Yu, Chen Yang, Chun-Lei Tang

{"title":"Concentration behavior of normalized ground states for mass critical Kirchhoff equations in bounded domains","authors":"Shubin Yu, Chen Yang, Chun-Lei Tang","doi":"arxiv-2409.05130","DOIUrl":"https://doi.org/arxiv-2409.05130","url":null,"abstract":"In present paper, we study the limit behavior of normalized ground states for\u0000the following mass critical Kirchhoff equation $$ left{begin{array}{ll}\u0000-(a+bint_{Omega}|nabla u|^2mathrm{d}x)Delta u+V(x)u=mu\u0000u+beta^*|u|^{frac{8}{3}}u &mbox{in} {Omega}, [0.1cm] u=0&mbox{on} {partialOmega}, [0.1cm] int_{Omega}|u|^2mathrm{d}x=1,\u0000[0.1cm] end{array} right. $$ where $ageq0$, $b>0$, the function $V(x)$ is\u0000a trapping potential in a bounded domain $Omegasubsetmathbb R^3$,\u0000$beta^*:=frac{b}{2}|Q|_2^{frac{8}{3}}$ and $Q$ is the unique positive\u0000radially symmetric solution of equation $-2Delta\u0000u+frac{1}{3}u-|u|^{frac{8}{3}}u=0.$ We consider the existence of constraint\u0000minimizers for the associated energy functional involving the parameter $a$.\u0000The minimizer corresponds to the normalized ground state of above problem, and\u0000it exists if and only if $a>0$. Moreover, when $V(x)$ attains its flattest\u0000global minimum at an inner point or only at the boundary of $Omega$, we\u0000analyze the fine limit profiles of the minimizers as $asearrow 0$, including\u0000mass concentration at an inner point or near the boundary of $Omega$. In\u0000particular, we further establish the local uniqueness of the minimizer if it is\u0000concentrated at a unique inner point.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Some applications of the Nehari manifold method to functionals in $C^1(X setminus {0})$ 内哈里流形方法在$C^1(Xsetminus {0})$中函数的一些应用

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI: arxiv-2409.05138

Edir Junior Ferreira Leite, Humberto Ramos Quoirin, Kaye Silva

引用次数: 0

On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains 关于迪里夏特分数拉普拉奇及其在有界域 SQG 方程中的应用

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI: arxiv-2409.05209

Elie Abdo, Quyuan Lin

引用次数: 0

Boundedness and finite-time blow-up in a repulsion-consumption system with flux limitation 具有通量限制的斥力-消耗系统中的有界性和有限时间膨胀

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI: arxiv-2409.05115

Ziyue Zeng, Yuxiang Li

{"title":"Boundedness and finite-time blow-up in a repulsion-consumption system with flux limitation","authors":"Ziyue Zeng, Yuxiang Li","doi":"arxiv-2409.05115","DOIUrl":"https://doi.org/arxiv-2409.05115","url":null,"abstract":"We investigate the following repulsion-consumption system with flux\u0000limitation begin{align}tag{$star$} left{ begin{array}{ll} u_t=Delta u+nabla cdot(uf(|nabla v|^2) nabla v), & x in Omega, t>0, tau v_t=Delta v-u v, & x in Omega, t>0, end{array} right. end{align} under no-flux/Dirichlet boundary conditions, where\u0000$Omega subset mathbb{R}^n$ is a bounded domain and $f(xi)$ generalizes the\u0000prototype given by $f(xi)=(1+xi)^{-alpha}$ ($xi geqslant 0$). We are\u0000mainly concerned with the global existence and finite time blow-up of system\u0000($star$). The main results assert that, for $alpha > frac{n-2}{2n}$, then\u0000when $tau=1$ and under radial settings, or when $tau=0$ without radial\u0000assumptions, for arbitrary initial data, the problem ($star$) possesses global\u0000bounded classical solutions; for $alpha<0$, $tau=0$, $n=2$ and under radial\u0000settings, for any initial data, whenever the boundary signal level large\u0000enough, the solutions of the corresponding problem blow up in finite time. Our results can be compared respectively with the blow-up phenomenon obtained\u0000by Ahn & Winkler (2023) for the system with nonlinear diffusion and linear\u0000chemotactic sensitivity, and by Wang & Winkler (2023) for the system with\u0000nonlinear diffusion and singular sensitivity .","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Adhesion and volume filling in one-dimensional population dynamics under Dirichlet boundary condition 迪里夏特边界条件下一维种群动力学中的粘附和体积填充

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-07 DOI: arxiv-2409.04689

Hyung Jun Choi, Seonghak Kim, Youngwoo Koh

引用次数: 0

Variational Dual Solutions for Incompressible Fluids 不可压缩流体的变分二元解法

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-07 DOI: arxiv-2409.04911

Amit Acharya, Bianca Stroffolini, Arghir Zarnescu

引用次数: 0

Holder regularity for nonlocal in time subdiffusion equations with general kernel 具有一般核的非局部时间亚扩散方程的荷尔德正则性

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-07 DOI: arxiv-2409.04841

Adam Kubica, Katarzyna Ryszewska, Rico Zacher

引用次数: 0