Global strong solutions for 3D viscous incompressible heat conducting magnetohydrodynamic flows with non-negative density

Existence of a Solution to the Non-Steady Magnetohydrodynamics-Boussinesq System with Mixed Boundary Conditions

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 ϵ and the Peclet number κ 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 ϵ and κ ( κ ≤ O ( ϵ β ) , 0 β ≤ 4 3 ), provided that the “well-prepared” initial condition for the solution and the non-slip boundary condition for the velocity are imposed.

Incompressible limit of non-isentropic compressible magnetohydrodynamic equations with zero magnetic diffusivity in bounded domains

We consider an initial boundary value problem for the nonhomogeneous heat conducting magnetohydrodynamic flows. We show that for the initial density allowing vacuum, the strong solution exists globally if the velocity field satisfies Serrin’s condition. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equations.

/pdf/serrin-type-blowup-criterion-of-three-dimensional-xnsnfwlxmv.pdf

Serrin-type blowup criterion of three-dimensional nonhomogeneous heat conducting magnetohydrodynamic flows with vacuum

Global well-posedness and decay estimates of strong solutions to the nonhomogeneous Boussinesq equations for magnetohydrodynamics convection

In this paper we establish the
 global existence of strong solution to the density-dependent incompressible magnetohydrodynamic equations with vaccum in a bounded domain
in $R^2$. Furthermore, the limit as the heat conductivity coefficient tends to zero is also obtained.

Global strong solution to the two-dimensional density-dependent magnetohydrodynamic equations with vaccum

In this paper we study the low Mach number limit of the full compressible Hall-magnetohydrodynamic (Hall-MHD) system in \begin{document}$\mathbb{T}^3$\end{document} . We prove that, as the Mach number tends to zero, the strong solution of the full compressible Hall-MHD system converges to that of the incompressible Hall-MHD system.

https://www.aimsciences.org/article/exportPdf?id=9738542f-b3e1-4121-a2aa-a6cc89c17dca

Low Mach number limit of the full compressible Hall-MHD system

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Global strong solution to the two-dimensional density-dependent magnetohydrodynamic equations with vaccum

Low Mach number limit of the full compressible Hall-MHD system