Stability of noncharacteristic boundary layers in the standing shock limit

2008/09/15 by Kevin Zumbrun, Zumbrun, Kevin · 1 citation
Engineering · Mathematics · #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #math.AP #msc:35B35

paper · pdf · doi:10.48550/arxiv.0809.2584

34 pp

arxiv created 2008/09/15 · arxiv updated 2009/12/01

Abstract

We investigate one- and multi-dimensional stability of noncharacteristic boundary layers in the limit approaching a standing planar shock wave U(x₁), x₁>0, obtaining necessary conditions of (i) weak stability of the limiting shock, (ii) weak stability of the constant layer u≡ U_-:=lim_{z→ -∞} U(z), and (iii) nonnegativity of a modified Lopatinski determinant similar to that of the inviscid shock case. For Lax 1-shocks, we obtain equally simple sufficient conditions; for p-shocks, p>1, the situation appears to be more complicated. Using these results, we determine stability of certain isentropic and full gas dynamical boundary-layers, generalizing earlier work of Serre--Zumbrun and Costanzino--Humphreys--Nguyen--Zumbrun.

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