数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (4): 1015-1029.

• 论文 • 上一篇    下一篇

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

金春花1, 杨彤2   

  1. 1 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    2 Department of Mathematics, City University of Hong Kong, Hong Kong, China
  • 收稿日期:2015-04-16 修回日期:2016-01-19 出版日期:2016-08-25 发布日期:2016-08-25
  • 通讯作者: Tong YANG,E-mail:matyang@cityu.edu.hk E-mail:matyang@cityu.edu.hk
  • 作者简介:Chunhua JIN,E-mail:jinchhua@126.com
  • 基金资助:

    C. Jin's research is supported by the Program for New Century Excellent Talents in University of the Ministry of Education (NCET-13-0804), NSFC (11471127), Guangdong Natural Science Funds for Distinguished Young Scholar (2015A030306029), The Excellent Young Teachers Program of Guangdong Province (HS2015007), Pearl River S&T Nova Program of Guangzhou (2013J2200064), and Special support program of Guangdong Province; T. Yang is supported by the General Research Fund of Hong Kong, CityU 104511.

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

Chunhua JIN1, Tong YANG2   

  1. 1 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    2 Department of Mathematics, City University of Hong Kong, Hong Kong, China
  • Received:2015-04-16 Revised:2016-01-19 Online:2016-08-25 Published:2016-08-25
  • Contact: Tong YANG,E-mail:matyang@cityu.edu.hk E-mail:matyang@cityu.edu.hk
  • Supported by:

    C. Jin's research is supported by the Program for New Century Excellent Talents in University of the Ministry of Education (NCET-13-0804), NSFC (11471127), Guangdong Natural Science Funds for Distinguished Young Scholar (2015A030306029), The Excellent Young Teachers Program of Guangdong Province (HS2015007), Pearl River S&T Nova Program of Guangzhou (2013J2200064), and Special support program of Guangdong Province; T. Yang is supported by the General Research Fund of Hong Kong, CityU 104511.

摘要:

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.

关键词: Time periodic solution, compressible Navier-Stokes equation, topology degree, energy method

Abstract:

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.

Key words: Time periodic solution, compressible Navier-Stokes equation, topology degree, energy method

中图分类号: 

  • 35Q30