Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1599-1611.

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Weak Solutions to Higher-Order Anisotropic Cahn-Hilliard-Navier-Stokes Systems

Jiao Luo(),Qian Qi(),Hong Luo*()   

  1. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066
  • Received:2020-06-03 Online:2020-12-26 Published:2020-12-29
  • Contact: Hong Luo;;
  • Supported by:
    the NSFC(10771306);the NSFC(11701399)


In this paper, we are concerned with weak solutions to higher-order anisotropic Cahn-Hilliard-Navier-Stokes systems in a two-dimensional bounded domain. The system consists of an incompressible Navier-Stokes equation coupled with a higher-order anisotropic Cahn-Hilliard equation. First some functional spaces and the definition of weak solutions are introduced. Then energy estimates of the solutions are given, and weak solutions of the system are obtained by Galerkin approximation scheme. Furthermore, the uniqueness of the solution to the system is proved.

Key words: Anisotropic, Cahn-Hilliard-Navier-Stokes system, Weak solutions, Existence, Uniqueness

CLC Number: 

  • O175.29