| A Condition of Boundary Layer Separation for 2-D Incompressible Magnetohydrodynamic Equations |
| Received:February 18, 2022 Revised:June 26, 2022 |
| Key Words:
Boundary layer separation Magnetohydrodynamic equations Incompressible flow Structural bifurcation
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12171343) and the Scientific Research Fund of the Science and Technology Department of Sichuan Province (Grant No.22CXTD0029). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2023.01.012 |
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