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Incompressible limit of non-isentropic compressible magnetohydrodynamic equations with zero magnetic diffusivity in bounded domains. (English) Zbl 1433.35292

Summary: This paper verifies the incompressible limit of the non-isentropic compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a three-dimensional bounded \(C^4\)-domain. The uniform estimates in both the Mach number \(\epsilon\) and the Péclet number \(\kappa\) for the local strong solutions, which exclude the estimate of high-order derivatives of the velocity in the normal directions to the boundary, are established in a short time interval independent of \(\epsilon\) and \(\kappa\) (\(\kappa \leq O(\epsilon^\beta)\), \(0 < \beta \leq \frac{4}{3}\)), provided that the “well-prepared” initial condition for the solution and the non-slip boundary condition for the velocity are imposed.

MSC:

35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35D35 Strong solutions to PDEs
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