三维非齐次不可压缩 MHD 方程组具边界的无粘极限问题

Abstract

Abstract:

This paper concerns the zero parameter limit problem for the 3-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with physical boundary conditions. In presence of the boundary, the velocity field and the magnetic field fulfill the vorticity-slip and the perfect insulating condition, respectively. We establish a global in time weak solution for the initial-boundary-value problem in general smooth bounded domain. Moreover, for a flat domain, the additional initial boundary condition $\nabla\rho_0\cdot n=0$ plays a very important role in the improving the regularity of the boundary condition and the proof of uniform regularity of the local strong solution. As the viscosity and magnetic dissipation tend to zero, we establish the higher-order convergence estimate with a rate in sense of $W^{2,p}(\Omega)$.

Key words: nonhomogeneous incompressible MHD equations, the zero parameter limit, boundary conditions

CLC Number:

O175.2

Pengfei Chen, Qinghan Chen. The Zero Parameter Limit for 3D Nonhomogeneous Incompressible MHD Equations with Boundary[J].Acta mathematica scientia,Series A, 2026, 46(5): 1667-1684.

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References 48

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The Zero Parameter Limit for 3D Nonhomogeneous Incompressible MHD Equations with Boundary

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