Navier-Stokes regularization of multidimensional Euler shocks

Olivier Guès (1) , Guy Metivier (2) , Mark Williams (3) , Kevin Zumbrun (4)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 IMB - Institut de Mathématiques de Bordeaux
3 Department of Mathematics [Chapel Hill]
4 Department of Mathematics IU

We establish existence and stability of multidimensional shock fronts in the vanishing viscosity limit for a general class of conservation laws with ``real'', or partially parabolic, viscosity including the Navier--Stokes equations of compressible gas dynamics with standard or van der Waals-type equation of state.

Mots clés: Shock front; viscous regularization; compressible Navier-Stokes equations; shock profile; Evans functions; stability

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Guès, Guy Metivier, Mark Williams, Kevin Zumbrun. Navier-Stokes regularization of multidimensional Euler shocks. Annales Scientifiques de l'École Normale Supérieure, 2006, 39, pp 75--175. ⟨hal-00113865⟩