Dynamics of Partial Differential Equations

Volume 16 (2019)

Number 2

Global regularity of the two-dimensional regularized MHD equations

Pages: 185 – 223

DOI: https://dx.doi.org/10.4310/DPDE.2019.v16.n2.a4


Zhuan Ye (Department of Mathematics and Statistics, Jiangsu Normal University, Jiangsu, China)


In this paper, we consider the Cauchy problem of the two-dimensional regularized incompressible magnetohydrodynamics equations. The main objective of this paper is to establish the global regularity of classical solutions of the magnetohydrodynamics equations with the minimal dissipation. Consequently, our results significantly improve the previous works.


MHD equations, global regularity, fractional dissipation

2010 Mathematics Subject Classification

Primary 35B65, 35Q35. Secondary 76D03.

Received 21 June 2018

Published 14 March 2019