Stability of multidimensional contact<br/><br/>discontinuities in compressible MHD

Monday, July 20, 2009 - 2:00pm - 2:50pm
EE/CS 3-180
Ya-Guang Wang (Shanghai Jiaotong University)
In this talk we study the stability of multidimensional contact discontinuities in compressible fluids. There are two kinds of contact discontinuities,
one is so-called the vortex sheet, mainly due to that the
tangential velocity is discontinuous across the front, and the other one is
the entropy wave, for which the velocity is continuous while the entropy
has certain jump on the front.

It is well-known that the vortex sheet in two dimensional compressible Euler equations is stable when the Mach number is larger than
√2, while in three dimensional problem it is always unstable. But,
some physical phenomena indicate that the magnetic field has certain
stabilization effect for waves in fluids. The first goal of this talk is
to rigorously justify this physical phenomenon, and to investigate the
stability of three-dimensional current-vortex sheet in compressible
magneto-hydrodynamics. By using energy method and the Nash-Moser iteration
scheme, we obtain that the current-vortex sheet in three-dimensional
compressible MHD is linearly and nonlinearly stable when the magnetic
fields on both sides of the front are non-parallel to each other.

The second goal is to study the stability of entropy waves. By a
simple computation, one can easily observe that the entropy wave is
structurally unstable in gas dynamics. By carefully studying
the effect
of magnetic fields on entropy waves, we obtain that the entropy wave in
three-dimensional compressible MHD is stable when the normal mag-
netic field is continuous and non-zero on the front.

This is a joint work with Gui-Qiang Chen.
MSC Code: