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We investigate one- and multi-dimensional stability of noncharacteristicboundary layers in the limit approaching a standing planar shock wave $\barU(x_1)$, $x_1>0$, obtaining necessary conditions of (i) weak stability of thelimiting shock, (ii) weak stability of the constant layer $u\equivU_-:=\lim_{z\to -\infty} \bar U(z)$, and (iii) nonnegativity of a modifiedLopatinski determinant similar to that of the inviscid shock case. For Lax1-shocks, we obtain equally simple sufficient conditions; for $p$-shocks,$p>1$, the situation appears to be more complicated. Using these results, wedetermine stability of certain isentropic and full gas dynamicalboundary-layers, generalizing earlier work of Serre--Zumbrun andCostanzino--Humphreys--Nguyen--Zumbrun.

Stability of noncharacteristic boundary layers in the standing shock limit