Regularity Criterion Of 3D Magnetic Bénard Equations And Liquid Crystal Equations

In this thesis,the criteria of the three-dimensional magnetic Bénard equations and liquid crystal equations are considered.Contents of this thesis are organized as follows:In the first part of chapter one,the research background and academic achievements of relevant scholars at home and abroad are introduced about the criteria of liquid crystal equations.In the second part,the research background and related achievements of blow-up criterion of solution of magnetic Bénard equations are introduced,and the conclusions of this thesis are also given.In chapter 2,the criteria of blow-up of the vertical derivative of the horizontal component of velocity in the three-dimensional liquid crystal equations are studied.In chapter 3,we proved the regularity criterion of velocity component and magnetic field component of the three-dimensional magnetic Bénard equations in Lorentz space.