Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

作者：Kwon Young-Sam^*; Lin Ying-Chieh; Su Cheng-Fang

来源：Journal of Nonlinear Science, 2018, 28(2): 599-620.

DOI：10.1007/s00332-017-9420-3

• Quasi-geostrophic equations
• Inviscid incompressible limit
• Magnetohydrodynamic flows

In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

• 出版日期2018-4