The Pressure Regularity Criteria Of The3D Magnetohydrodynamic Equations

Since Faraday first raised about some issues of MHD (Magnetohydro dynamic, MHD) equations in1832, The theoretical and computational studies have been large explored by more and more researchers [1-49]. As an important fluid of the fluid dynamics, MHD considers the interaction between the electromagnetic field and the electrically conductive fluid flows. It is mainly used in physics sciences and the new energy technologies and so on. In mathematics, especially in the fields of the nonlinear Partial differential equations, is is also of great significance to study the MHD equations as a nonlinear partial differential equations. The main purpose of this thesis is to consider pressure regularity criteria for Cauchy problem of the three-dimensional MHD equations.In the chapter1, after introducing the fundamental physical background of mag-netohydrodynamic equations, we first recalled the related previous work on the pressure regularity criteria of magnetohydrodynamic equations. Secondly, we gave some prelimi-nary which is necessary in this thesis.In the chapter2,we consider the pressure regularity criteria of three-dimension mag-netohydrodynamic equations under the case0<s<1.which mainly applied to some well-known inequalities, the basic idea has use the Littlewood-Paley decomposition. If the pressure n(x, t) satisfies then (v, b) is smooth on (0, T].In the chapter3,we consider the pressure regularity criteria of three-dimension mag-netohydrodynamic equations under the case s=0. The argument is mainly similar to those inequalities in Chapter two and also uses Littlewood-Paley decomposition method. If the pressure n(x, t) satisfies then (v,b) is smooth on (0,T).