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arXiv · 1912.11924

Well-Posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics

Yuri Trakhinin·Tao Wang
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Abstract

We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma--vacuum interface. We establish the local-in-time existence and uniqueness of solutions to this nonlinear characteristic hyperbolic problem under the Rayleigh--Taylor sign condition on the total pressure. The proof is based on certain tame estimates in anisotropic Sobolev spaces for the linearized problem and a modification of the Nash--Moser iteration scheme. Our result is uniform in the light speed and appears to be the first well-posedness result for the free boundary problem in ideal compressible magnetohydrodynamics with zero total pressure on the moving boundary.

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Yuri Trakhinin, Tao Wang. 2019-12-26. Well-Posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics. https://doi.org/10.1007/s00205-020-01592-6

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