Well-posedness of the linearized MHD-Maxwell free boundary problem
Year: 2013
Type: preprint
Abstract: We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free-interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary.
The aim of this paper is the study of the stability of the linearized problem with variable coefficients for nonplanar plasma-vacuum interfaces. Under suitable stability conditions satisfied at each point of the plasma-vacuum interface, we derive a basic a priori estimate for solutions to the linearized problem in the Sobolev space $H^1_{\tan}$ with conormal regularity. The proof follows by a suitable secondary symmetrization of the Maxwell equations in vacuum and the energy method.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W204398619