Regularity Criteria For The 3D Axially Symmetric MHD Equations

Incompressible magnetohydrodynamic(MHD)equations describe the basic laws of mechanics for the movement of conducting fluids.They are widely used in the area of plasma,astronomy,engineering,etc.This thesis is concerned with the regularity criteria of the axisymmetric weak solutions to the incompressible MHD equations.Some weighted regularity criteria in terms of the swirl component of velocity and magnetic fields,and the radial component of velocity field or swirl component of vorticity are established for a special magnetic field by making use of the maximum principle,weighted L? estimate of the velocity and magnetic fields,the theory of singular integral operators and Sobolev-Hardy inequalities.