二维不可压缩磁流体方程边界层分离的条件

A Condition of Boundary Layer Separation for 2-D Incompressible Magnetohydrodynamic Equations

中文关键词:  边界层分离  磁流体方程  不可压缩流  结构分歧

英文关键词:Boundary layer separation  Magnetohydrodynamic equations  Incompressible flow  Structural bifurcation

中文摘要:

      该文研究了二维不可压缩磁流体方程的解,其中要求磁流体的速度满足Dirichlet边界条件、磁场在边界上的值与时间无关. 利用Taylor展开式和不可压缩流的结构分歧理论, 得到了磁流体方程发生边界层分离的条件, 它取决于外力、初值和磁场在边界上的取值, 并且该条件可以预测磁流体边界层分离发生的时间与地点.

英文摘要:

      In this paper, we consider the solutions of 2-D incompressible magnetohydrodynamic (MHD) equations with homogenous Dirichlet boundary condition for velocity and with nonhomogenous Dirichlet boundary condition for magnetic field. We obtain a condition of boundary layer separation by Taylor expansion of functions in the MHD equations and by structural bifurcation theory for divergence free flows with Dirichlet boundary conditions. Furthermore, the condition, determined by external forces, initial values and the value of magnetic field on the boundary, can predict when and where boundary layer separation for the magnetic fluid will occur.