Global regularity of 2D MHD equations with almost Laplacian velocity dissipation

Abstract

Abstract We obtain the global existence and global regularity for the 2D MHD equations with almost Laplacian velocity dissipation, which require the dissipative operators weaker than any power of the fractional Laplacian. The result can be regarded as a further improvement and generalization of previous works.

Keywords

• Generalized magnetohydrodynamic equations
• Global regularity
• Viscous flow
• Sobolev imbedding