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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Stability of the linearized MHD-Maxwell free inter
face problem - Secchi\, P (Universit degli Studi d
i Brescia)
DTSTART;TZID=Europe/London:20140522T151500
DTEND;TZID=Europe/London:20140522T161500
UID:TALK52715AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52715
DESCRIPTION:In the talk we consider the free boundary problem
for the plasma-vacuum interface in ideal compressi
ble magnetohydrodynamics (MHD). In the plasma regi
on\, the flow is governed by the usual compressibl
e MHD equations\, while in the vacuum region we co
nsider the Maxwell system for the electric and the
magnetic fields\, in order to investigate the we
ll-posedness of the problem\, in particular in rel
ation with the electric field in vacuum. At the fr
ee interface\, driven by the plasma velocity\, the
total pressure is continuous and the magnetic fie
ld on both sides is tangent to the boundary.\nUnde
r suitable stability conditions satisfied at each
point of the plasma-vacuum interface\, we derive a
basic a priori estimate for solutions to the li
nearized problem in the Sobolev space $H^1_{ an}$
with conormal regularity. The proof follows by a s
uitable secondary symmetrization of the Maxwell eq
uations in vacuum and the energy method.\nAn inter
esting novelty is represented by the fact that the
interface is characteristic with variable multipl
icity\, so that the problem requires a different n
umber of boundary conditions\, depending on the di
rection of the front velocity (plasma expansion in
to vacuum or viceversa). To overcome this difficul
ty\, we recast the vacuum equations in terms of a
new variable which makes the interface characteris
tic of constant multiplicity. In particular\, we d
on't assume that plasma expands into vacuum.\nThis
is a joint work with D.Catania and M.D'Abbicco.\n
\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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