Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

Abstract

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in ${\mathbb{R}}^n$ for $n=2,3$. In comparison with the work of the 3D fractional Navier-Stokes equations obtained by Tang and Yu in [24, Commun. Math. Phys. 334: 1455--1482, 2015], our results include their endpoint case $\alpha =3/4$ and the external force belongs to more general parabolic Morrey space. Moreover, we prove some interior regularity criteria just via the scaled mixed norm of the velocity for the suitable weak solutions to the fractional MHD equations.

33 pages

References in corpus (3)

• On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations
• Global Regularity of 2D Generalized MHD Equations with Magnetic Diffusion
• Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

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• On Wolf's regularity criterion of suitable weak solutions to the Navier-Stokes equations
• Partial regularity for the steady hyperdissipative fractional Navier-Stokes equations
• Global existence of uniformly locally energy solutions for the incompressible fractional Navier-Stokes equations
• A $\epsilon$-regularity criterion without pressure of suitable weak solutions to the Navier-Stokes equations at one scale