Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1361-1372.doi: 10.1016/S0252-9602(17)30078-4

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EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION TO THE INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ MODELIN 2-DIMENSION

Guangwu WANG1, Boling GUO2   

  1. 1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China Graduate School of China Academy of Engineering Physics, Beijing 100088, China;
    2. Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing 100088, China
  • Received:2016-03-20 Revised:2016-09-13 Online:2017-10-25 Published:2017-10-25
  • Contact: Guangwu WANG,E-mail:yunxianwgw@163.com E-mail:yunxianwgw@163.com

Abstract:

In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy. The main techniques is the Faedo-Galerkin approximation and weak compactness theory.

Key words: global finite energy weak solution, incompressible Navier-Stokes-Landau-Lifshitz system, Faedo-Galerkin method

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