Conditional Stability of Unstable Viscous Shock Waves in Compressible Gas Dynamics and MHD

被引:2
|
作者
Zumbrun, Kevin [1 ]
机构
[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA
基金
美国国家科学基金会;
关键词
HYPERBOLIC-PARABOLIC SYSTEMS; NONLINEAR BOUNDARY-CONDITIONS; PROFILES; INSTABILITY; BIFURCATION; VISCOSITY; MANIFOLDS;
D O I
10.1007/s00205-010-0359-x
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic-parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small L (1) a (c) H (3) perturbations, converging time asymptotically to a translate of the unperturbed wave. That is, for a shock with p unstable eigenvalues, we establish conditional stability on a codimension-p manifold of initial data, with sharp rates of decay in all L (p) . For p = 0, we recover the result of unconditional stability obtained by Mascia and Zumbrun. The main new difficulty in the hyperbolic-parabolic case is to construct an invariant manifold in the absence of parabolic smoothing.
引用
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页码:1031 / 1056
页数:26
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