Global Strong Solution of a 2D coupled Parabolic-Hyperbolic Magnetohydrodynamic System

Ruikuan Liu; Jiayan Yang

Global Strong Solution of a 2D coupled Parabolic-Hyperbolic Magnetohydrodynamic System

Analysis of PDEs 2017-01-31 v1

Authors: Ruikuan Liu , Jiayan Yang

Abstract

The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic (MHD) model in two dimensional space. Based on Agmon, Douglis and Nirenberg's estimates for the stationary Stokes equation and the Solonnikov's theorem of $L^p$ - $L^q$ -estimates for the evolution Stokes equation, it is shown that the mixed-type MHD equations exist a global strong solution.

Keywords

global strong solution parabolic-hyperbolic system incompressible magnetohydrodynamic two-dimensional space Stokes equation mixed-type MHD equations

Cite

@article{arxiv.1701.08353,
  title  = {Global Strong Solution of a 2D coupled Parabolic-Hyperbolic Magnetohydrodynamic System},
  author = {Ruikuan Liu and Jiayan Yang},
  journal= {arXiv preprint arXiv:1701.08353},
  year   = {2017}
}

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13 pages

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