2006/07/03 by Olivier Guès, Olivier Gues, Gues, Olivier +6
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics #Navier-Stokes equation solutions #math.AP #msc:35L60
paper · pdf · doi:10.48550/arxiv.math/0607065
arxiv created 2006/07/03 · arxiv updated 2009/12/01
Extending investigations of Métivier&Zumbrun in the hyperbolic case, we treat stability of viscous shock and boundary layers for viscous perturbations of multidimensional hyperbolic systems with characteristics of variable multiplicity, specifically the construction of symmetrizers in the low-frequency regime where variable multiplicity plays a role. At the same time, we extend the boundary-layer theory to ``real'' or partially parabolic viscosities, Neumann or mixed-type parabolic boundary conditions, and systems with nonconservative form, in addition proving a more fundamental version of the Zumbrun--Serre--Rousset theorem, valid for variable multiplicities, characterizing the limiting hyperbolic system and boundary conditions as a nonsingular limit of a reduced viscous system. The new effects of viscosity are seen to be surprisingly subtle; in particular, viscous coupling of crossing hyperbolic modes may induce a destabilizing effect. We illustrate the theory with applications to magnetohydrodynamics.