Regularity Criteria Of The Solutions To Axisymmetric Magnetohydrodynamic System

In this thesis,we consider the regularity criteria of solutions for the three dimensional axially symmetric Magnetohydrodynamic(MHD)equations.By using the energy method we obtain the global regularity of the solutions under the assumption that the curl components of the velocity vector and the magnetic field vector satisfy certain space-time conditions.In chapter 1,we briefly introduce the research background and research of classical incompressible Magnetohydrodynamic(MHD)equations.In chapter 2,we present the relationship between Cartesian coordinate and Cylindrical coordinate.Then we apply cylindrical coordinate transformation to the MHD equations in Cartesian coordinate to derive the axisymmetric MHD equations.In chapter 3,we establish the energy estimate of r~3?_?,r~3n_?.In chapter 4,the global well-posedness of solutions for the axisymmetric MHD equations are explored.By using the energy estimate,we obtained that if the curl component satisfies a suitable condition,the axially symmetric MHD equations are globally well-posed.