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

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (4): 1015-1029.

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

Chunhua JIN¹, Tong YANG²

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.

Abstract

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

CLC Number:

35Q30

Chunhua JIN, Tong YANG. TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN[J].Acta mathematica scientia,Series B, 2016, 36(4): 1015-1029.

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References

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

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