ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

doi:10.1007/s10473-019-0114-9

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 165-179.doi: 10.1007/s10473-019-0114-9

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

程峰¹, 徐超江^2,3

1. Hubei Key Laboratory of Applied Mathematics;School of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
3. Universitéde Rouen, CNRS UMR 6085, Laboratoire de Mathématiques, 76801 Saint-Etienne du Rouvray, France

收稿日期:2017-09-19 修回日期:2018-05-20 出版日期:2019-02-25 发布日期:2019-03-13
通讯作者: Feng CHENG E-mail:fengcheng@hubu.edu.cn
作者简介:Chaojiang XU, Chao-Jiang.Xu@univ-rouen.fr
基金资助:
The research of the second author was supported partially by "The Fundamental Research Funds for Central Universities of China".

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

Feng CHENG¹, Chaojiang XU^2,3

1. Hubei Key Laboratory of Applied Mathematics;School of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
3. Universitéde Rouen, CNRS UMR 6085, Laboratoire de Mathématiques, 76801 Saint-Etienne du Rouvray, France

Received:2017-09-19 Revised:2018-05-20 Online:2019-02-25 Published:2019-03-13
Contact: Feng CHENG E-mail:fengcheng@hubu.edu.cn
Supported by:
The research of the second author was supported partially by "The Fundamental Research Funds for Central Universities of China".

摘要/Abstract

摘要： In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H¹-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

关键词: analyticity, smoothing effect of solutions, Boussinesq equation

Abstract: In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H¹-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

Key words: analyticity, smoothing effect of solutions, Boussinesq equation

程峰, 徐超江. ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(1): 165-179.

Feng CHENG, Chaojiang XU. ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS[J]. Acta mathematica scientia,Series B, 2019, 39(1): 165-179.

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ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

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