Global regularity of the two-dimensional Boussinesq equations without diffusivity in bounded domains

被引：3

作者：

Zhou, Daoguo ^{[1
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 43卷

基金：

中国国家自然科学基金;

关键词：

Global regularity; Boussinesq equations; Zero diffusivity; Bounded domain; THERMAL-DIFFUSIVITY; WELL-POSEDNESS; PARTIAL VISCOSITY; SYSTEM; PERSISTENCE;

D O I：

10.1016/j.nonrwa.2018.02.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We address the well-posedness for the two-dimensional Boussinesq equations with zero diffusivity in bounded domains. We prove global in time regularity for rough initial data: the initial velocity has epsilon fractional derivatives in L-q and the initial temperature is in L-q, for some q > 2 and epsilon > 0 arbitrarily small. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：144 / 154

页数：11

共 25 条

[1] On the global well-posedness for Boussinesq system [J].

Abidi, H. ;

Hmidi, T. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 233 (01) :199-220

[2] Global regularity results for the 2D Boussinesq equations with vertical dissipation [J].

Adhikari, Dhanapati ;

Cao, Chongsheng ;

Wu, Jiahong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (06) :1637-1655

[3]

[Anonymous], 2003, SOBOLEV SPACES

[4]

Ao Ladyzhenskaya O., 1970, Mathematical problems in the dynamics of a viscous incompressible fluid

[5] Global regularity for the 2D Boussinesq equations with partial viscosity terms [J].

Chae, Dongho .

ADVANCES IN MATHEMATICS, 2006, 203 (02) :497-513

[6] Density-dependent incompressible fluids in bounded domains [J].

Danchin, R. .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2006, 8 (03) :333-381

[7] The Leray and Fujita-Kato theorems for the Boussinesq system with partial viscosity [J].

Danchin, Raphael ;

Paicu, Marius .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2008, 136 (02) :261-309

[8]

Desjardins B., 1997, Differ. Int. Equ, V10, P577

[9] Smoothing estimates of 2d incompressible Navier-Stokes equations in bounded domains with applications [J].

He, Lingbing .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (07) :3430-3464

[10]

Hou TY, 2005, DISCRETE CONT DYN-A, V12, P1

← 1 2 3 →