Communications in Mathematical Sciences

Volume 14 (2016)

Number 3

Time periodic solutions to the 3D compressible fluid models of Korteweg type

Pages: 705 – 733



Zhong Tan (School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen, China)

Qiuju Xu (School of Mathematical Sciences, Xiamen University, Xiamen, China)


This paper is concerned with time periodic solutions to the three-dimensional compressible fluid models of Korteweg type under some smallness and structure conditions on a time periodic force. The proof is based on a regularized approximation scheme and the topological degree theory for time periodic solutions in a bounded domain. Furthermore, via a limiting process, the existence results can be obtained in the whole space.


3D compressible Navier–Stokes–Korteweg system, time periodic solutions, uniform estimates, topological degree theory

2010 Mathematics Subject Classification

35B10, 35M10, 35Q35

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Published 26 February 2016