The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion

Abstract

This paper examines the global (in time) regularity of classical solutions to the 2D incompressible magnetohydrodynamics (MHD) equations with only magnetic diffusion. Here the magnetic diffusion is given by the fractional Laplacian operator $(-\Delta {)}^{\beta }$. We establish the global regularity for the case when $\beta >1$. This result significantly improves previous work which requires $\beta >\frac{3}{2}$ and brings us closer to the resolution of the well-known global regularity problem on the 2D MHD equations with standard Laplacian magnetic diffusion, namely the case when $\beta =1$.

16 pages

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Cited by in corpus (4)

• On the global regularity of two-dimensional generalized magnetohydrodynamics system
• A remark on the two-dimensional magneto-hydrodynamics-alpha system
• Global small solution to the 2D MHD system with a velocity damping term
• On the Decay and Stability of Global Solutions to the 3D Inhomogeneous MHD system