Dynamics of Partial Differential Equations

Volume 15 (2018)

Number 1

On the inviscid limit of the 2D Magnetohydrodynamic system with vorticity in Yudovich-type space

Pages: 61 – 80

DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n1.a3

Authors

Qionglei Chen (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Huan Yu (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Abstract

In this paper, we first prove the existence and uniqueness of solutions only with magnetic diffusion for the vorticity being Yudovich-type space, by establishing some new time weighted estimates of the magnetic field, which improves the corresponding results of C. Cao, J. Wu and B. Yuan [5], and of Q. Jiu and J. Zhao [16]. Furthermore, we prove a global result on the inviscid limit of the two-dimensional Magnetohydrodynamic equations with data belonging to the Yudovich type.

Keywords

Magnetohydrodynamic equations, magnetic diffusion, global wellposedness, Yudovich data

2010 Mathematics Subject Classification

35B35, 35Q35, 76D05

Full Text (PDF format)

Chen was partially supported by the National Natural Science Foundation of China No. 11671045. Yu was partially supported by the National Natural Science Foundation of China No. 11671273.

Received 28 October 2016

Published 14 December 2017