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arXiv · 2007.02607

On the vanishing dissipation limit for the incompressible MHD equations on bounded domains

Qin Duan·Yuelong Xiao·Zhouping Xin
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Abstract

In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field fulfills a Navier-slip condition, while the magnetic field satisfies the insulating condition. It is shown that the initial-boundary problem has a global weak solution for a general smooth domain. More importantly, for a flat domain, we establish the uniform local well-posedness of the strong solution with higher order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD as the dissipation tends to zero.

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Qin Duan, Yuelong Xiao, Zhouping Xin. 2020-07-06. On the vanishing dissipation limit for the incompressible MHD equations on bounded domains. https://arxiv.org/abs/2007.02607

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