Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional stability of unstable viscous shock waves in compressible
  gas dynamics and MHD   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 $L^1\cap H^3$ 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.

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The categories of this paper are: quant-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: stat