Local Well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics

DOI10.1007/S00526-023-02462-1arXiv2012.13931MaRDI QIDQ6357012

Publication date: 27 December 2020

Abstract: We prove the local well-posedness in Sobolev spaces of the free-boundary problem for compressible inviscid resistive isentropic MHD system under the Rayleigh-Taylor physical sign condition, which describes the motion of a free-boundary compressible plasma in an electro-magnetic field with magnetic diffusion. We use Lagrangian coordinates and apply the tangential smoothing method introduced by Coutand-Shkoller to construct the approximation solutions. One of the key observations is that the Christodoulou-Lindblad type elliptic estimate together with magnetic diffusion not only gives the common control of magnetic field and fluid pressure directly, but also controls the Lorentz force which is a higher order term in the energy functional.

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Free boundary problems for PDEs (35R35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

This page was built for publication: Local Well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6357012)