LOCAL STRONG SOLUTIONS TO THE NONHOMOGENEOUS BENARD SYSTEM WITH NONNEGATIVE DENSITY

被引：8

作者：

Zhong, Xin ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2020年 / 50卷 / 04期

关键词：

nonhomogeneous Benard system; strong solutions; Cauchy problem; nonnegative density; GLOBAL WELL-POSEDNESS; NAVIER-STOKES EQUATIONS; EXISTENCE; BOUNDARY;

D O I：

10.1216/rmj.2020.50.1497

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Cauchy problem of the nonhomogeneous Benard system in the whole two-dimensional (2D) space, where the density is allowed to vanish initially. We prove that there exists a unique local strong solution. To compensate for the lack of integrability of the velocity in the whole space, a careful space weight is imposed on the initial density, which cannot decay too slowly in the far field.

引用

页码：1497 / 1516

页数：20

共 50 条

[41] Strong solutions for the nonhomogeneous Navier-Stokes equations in unbounded domains
Braz e Silva, P.
Rojas-Medar, M. A.
Villamizar-Roa, E. J.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2010, 33 (03) : 358 - 372
[42] Global strong solutions to the nonhomogeneous incompressible MHD equations in a bounded domain
Fan, Jishan
Li, Fucai
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2019, 46 : 1 - 11
[43] LOCAL AND GLOBAL ESTIMATES OF DERIVATIVES OF THE NONHOMOGENEOUS HYPOELLIPTIC EQUATION SOLUTIONS
BURENKOV, VI
MAMAN, KR
DOKLADY AKADEMII NAUK SSSR, 1987, 294 (04): : 777 - 781
[44] EXISTENCE AND NONEXISTENCE OF LOCAL/GLOBAL SOLUTIONS FOR A NONHOMOGENEOUS HEAT EQUATION
Li, Xie
Xiang, Zhaoyin
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (04) : 1465 - 1480
[45] Global existence and exponential decay of strong solutions for 2D nonhomogeneous micropolar fluids with density-dependent viscosity
Liu, Lingxi
Zhong, Xin
JOURNAL OF MATHEMATICAL PHYSICS, 2021, 62 (06)
[46] Density of diluted solutions of strong electrolytes
Sauter, F
ZEITSCHRIFT FUR PHYSIKALISCHE CHEMIE-ABTEILUNG A-CHEMISCHE THERMODYNAMIK KINETIK ELEKTROCHEMIE EIGENSCHAFTSLEHRE, 1941, 188 (04): : 229 - 234
[47] Strong solutions to the nonhomogeneous Boussinesq equations for magnetohydrodynamics convection without thermal diffusion
Zhong, Xin
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2020, (24) : 1 - 23
[48] Global strong solutions for nonhomogeneous heat conducting Navier-Stokes equations
Zhong, Xin
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (01) : 127 - 139
[49] Normalized solutions for coupled Schrodinger system with nonhomogeneous nonlinearity
Shen, Chunyu
Tian, Yaqi
Zhou, Haifang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 519 (01)
[50] On the existence of solutions for nonhomogeneous Schrodinger-Poisson system
Wang, Lixia
Ma, Shiwang
Wang, Xiaoming
BOUNDARY VALUE PROBLEMS, 2016,

← 1 2 3 4 5 →