Stability of noncharacteristic boundary layers in the standing shock limit

Details Stability of noncharacteristic boundary layers in the standing shock limit Stability of noncharacteristic boundary layers in the standing shock limit

2008-09-15

arxiv.org/abs/0809.2584v1

Mathematics

Analysis of PDEs

34 pp

Scientific paper

We investigate one- and multi-dimensional stability of noncharacteristic boundary layers in the limit approaching a standing planar shock wave $\bar U(x_1)$, $x_1>0$, obtaining necessary conditions of (i) weak stability of the limiting shock, (ii) weak stability of the constant layer $u\equiv U_-:=\lim_{z\to -\infty} \bar U(z)$, 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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