| 二维不可压缩磁流体方程边界层分离的条件 |
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| 引用本文： | 胡碧艳,胡凯伦,罗宏. 二维不可压缩磁流体方程边界层分离的条件[J]. 数学研究及应用, 2023, 43(1): 109-115 |
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| 作者姓名： | 胡碧艳 胡凯伦 罗宏 |
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| 作者单位： | 四川师范大学数学科学学院, 四川 成都 610068 |
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| 基金项目： | 国家自然科学基金(Grant No.12171343),四川省科技厅科研基金(Grant No.22CXTD0029). |
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| 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.
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| 关 键 词： | 边界层分离 磁流体方程 不可压缩流 结构分歧 |
| 收稿时间： | 2022-02-18 |
| 修稿时间： | 2022-06-26 |
A Condition of Boundary Layer Separation for 2-D Incompressible Magnetohydrodynamic Equations |
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| Biyan HU,Kailun HU,Hong LUO. A Condition of Boundary Layer Separation for 2-D Incompressible Magnetohydrodynamic Equations[J]. Journal of Mathematical Research with Applications, 2023, 43(1): 109-115 |
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| Authors: | Biyan HU Kailun HU Hong LUO |
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| Affiliation: | School of Mathematical Sciences, Sichuan Normal University, Sichuan 610068, P. R. China |
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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. |
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| Keywords: | Boundary layer separation Magnetohydrodynamic equations Incompressible flow Structural bifurcation |
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