Regularity Criteria For The Three-dimensional MHD Equations

Usually§we hope the solutions of the Partial Di?erential Equations to besmooth enough to qualify as a classical solution. This leads to the study of regu-larity of weak solutions.As we all know, the existence of weak solutions dependson simple estimates plus idea of functional analysis, whereas the regularity of theweak solutions , when true, usually rests upon many intricate calculus estimates.In this paper, by using some classical inequalities, we consider regularitycriteria for solutions to the 3D MHD equations with incompressible conditionsand obtain a new result.This article is divided into 4 chapters. Chapter 1 is introduction. Chapter2 is the preliminaries needed in the proofs of the conclusions. In Chapter 3, weprove the regularity criterion for solutions of three-dimensional MHD equationswith incompressible conditions. Finally, we conclude in Chapter 4 and give somecomments on possible future work.