Global weak solutions of 3D compressible MHD with discontinuous initial data and vacuum

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Liu, Shengquan^1,2  Yu, Haibo¹  Zhang, Jianwen¹ 

[1] Xiamen Univ, Sch Math Sci, Xiamen 351005, Peoples R China

[2] Liaoning Univ, Dept Math, Shenyang 110036, Peoples R China

关键词: Compressible magnetohydrodynamics;    Vacuum;    Large oscillation;    Global weak solution;    Large-time behavior;   

DOI  :  10.1016/j.jde.2012.08.006

来源: Elsevier

【 摘 要 】

In this paper, we study the global existence of weak solutions to the Cauchy problem of the three-dimensional equations for compressible isentropic magnetohydrodynamic flows subject to discontinuous initial data. It is assumed here that the initial energy is suitably small in L-2, and that the initial density and the gradients of initial velocity/magnetic field are bounded in L-infinity and L-2, respectively. This particularly implies that the initial data may contain vacuum states and the oscillations of solutions could be arbitrarily large. As a byproduct, we also prove the global existence of smooth solutions with strictly positive density and small initial energy. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free