涉及水平分量的磁场微极流方程组的正则性准则

Regularity Criteria for Magneto-Micropolar Fluid Equations in Terms of Horizontal Components

磁场微极流方程组是不可压缩流体力学方程组中的一个相当完备的系统,在某些特定的条件下可以退化成非常经典的方程组,如Navier-Stokes方程组、Magneto-hydrodynamics方程组等。现研究水平速度场和磁场与三维磁场微极流方程组光滑解的整体存在性之间的关系,将Navier-Stokes方程组的相关成果推广到磁场微极流方程组,使得相应的结果在微极流方程组和MHD方程组中都成立。

Magneto-Micropolar fluid is a fairly complete system of the incompressible hydrodynamic equations, and can be degenerated into classic equations under certain specific conditions, such as Navier-Stokes equations, MHD equations, etc.We concern the relations and global existence between the horizontal components of the velocity and magnetic field and the smooth solutions of the 3D Magneto-Micropolar fluid. We extend the results of Navier-Stokes equations to Magneto-Micropolar fluid equations. Our results have inclusion relation to micropolar fluid equations and Magneto-hydrodynamics equations.