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SUMMARY:Stability of the linearized MHD-Maxwell free interface problem - S
 ecchi\, P (Universit degli Studi di Brescia)
DTSTART:20140522T141500Z
DTEND:20140522T151500Z
UID:TALK52715@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In the talk we consider the free boundary problem for the plas
 ma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In t
 he plasma region\, the flow is governed by the usual compressible MHD equa
 tions\, while in the vacuum region we consider the Maxwell system for the 
 electric and the magnetic fields\, in order to investigate  the well-posed
 ness 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.\nUnder suitable stability conditions satisfied at each poin
 t of the plasma-vacuum interface\, we derive a basic a priori estimate  fo
 r solutions to the  linearized problem in the Sobolev space $H^1_{	an}$ wi
 th conormal regularity. The proof follows by a suitable secondary symmetri
 zation of the Maxwell equations in vacuum and the energy method.\nAn inter
 esting novelty is represented by the fact that the interface is characteri
 stic with variable multiplicity\, so that the problem requires a different
  number of boundary conditions\, depending on the direction of the front v
 elocity (plasma expansion into vacuum or viceversa). To overcome this diff
 iculty\, we recast the vacuum equations in terms of a new variable which m
 akes the interface characteristic of constant multiplicity. In particular\
 , we don't assume that plasma expands into vacuum.\nThis is a joint work w
 ith D.Catania and M.D'Abbicco.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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