Global well-posedness to the 3D incompressible MHD equations with a new class of large initial data

Abstract

We obtain the global well-posedness to the 3D incompressible magnetohydrodynamics (MHD) equations in Besov space with negative index of regularity. Particularly, we can get the global solutions for a new class of large initial data. As a byproduct, this result improves the corresponding result in \cite{HHW}. In addition, we also get the global result for this system in ${\chi }^{-1}({\mathbb{R}}^3)$ originally developed in \cite{LL}. More precisely, we only assume that the norm of initial data is exactly smaller than the sum of viscosity and diffusivity parameters.

arXiv commentSubmitted,15 pages

References in corpus (2)

• On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations
• On the uniqueness for the 2D MHD equations without magnetic diffusion

Cited by in corpus (1)

• A class of global large, smooth solutions for the magnetohydrodynamics with the Hall and ion-slip effects