Multidimensional stability of viscous shock waves for symmetric systems

Long-time nonlinear stability of multi-dimensional viscous shocks of a general class of symmetric hyperbolic--parabolic systems in dimensions $d\geq 2$ will be discussed. The stability under the so--called Evans function condition has been well established by Kevin Zumbrun and his collaborators for the last twelve years. We shall briefly review these results and present some recent developments, extending the results to a larger class of symmetric systems and weakening/dropping certain technical assumptions. We make use of the highly technical construction of Kreiss' symmetrizers by O. Guès, G. Métivier, M. Williams, and K. Zumbrun.