Global stability of large solutions of the 3-D compressible magnetohydrodynamic equations

作者：Chen Yuhui; Huang Jingchi^*; Xu Haiyan

来源：Nonlinear Analysis: Real World Applications , 2019, 47: 272-290.

DOI：10.1016/j.nonrwa.2018.11.001

• Compressible magnetohydrodynamic
• Large solutions
• Stability

The current paper is devoted to the investigation of the global-in-time stability of large solutions to the compressible Magnetohydrodynamic equations in the whole space. Suppose that the density and the magnetic field are bounded from above uniformly in time in the Holder space C-alpha with alpha sufficiently small and in L-infinity space respectively. Then we prove two results: (1). Such kind of the solution will converge to its associated equilibrium with a rate which is the same as that for the heat equation. (2). Such kind of the solution is stable, which means any perturbed solution will remain close to the reference solution if initially they are close to each other. This implies that the set of the smooth and bounded solutions is open.

• 单位
  广东工业大学