Global Regularity of 2D Generalized MHD Equations with Magnetic Diffusion

Abstract

This paper is concerned with the global regularity of the 2D (two-dimensional) generalized magnetohydrodynamic equations with only magnetic diffusion ${\Lambda }^{2\beta }b$. It is proved that when $\beta >1$ there exists a unique global regular solution for this equations. The obtained result improves the previous known one which requires that $\beta >\frac{3}{2}$.

6 pages

References in corpus (1)

• Well-posedness of the Cauchy problem for the fractional power dissipative equations

Cited by in corpus (4)

• Global classical solutions of 2D MHD system with only magnetic diffusion on periodic domain
• Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations
• A class large solution of the 2D MHD equations with velocity and magnetic damping
• On the global well-posedness of the 3D axisymmetric resistive MHD equations