TITLE

ABILITY OF THE LINEARIZED MHD-MAXWELL FREE INTERFACE PROBLEM

AUTHOR(S)
CATANIA, DAVIDE; D'ABBICCO, MARCELLO; SECCHI, PAOLO; Kukavica, Igor
PUB. DATE
November 2014
SOURCE
Communications on Pure & Applied Analysis;Nov2014, Vol. 13 Issue 6, p2407
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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, in order to investigate the well-posedness of the problem, in particular in relation with the electric field in vacuum. 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. 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 Htan¹ with conormal regularity. The proof follows by a suitable secondary symmetrization of the Maxwell equations in vacuum and the energy method. An interesting novelty is represented by the fact that the interface is characteristic with variable multiplicity, so that the problem requires a different number of boundary conditions, depending on the direction of the front velocity (plasma expansion into vacuum or viceversa). To overcome this difficulty, we recast the vacuum equations in terms of a new variable which makes the interface characteristic of constant multiplicity. In particular, we don't assume that plasma expands into vacuum.
ACCESSION #
97869290

 

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