Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Stability of Compressible Vortex Sheets in Two-Dimensional
  Elastodynamics   The linear stability of rectilinear compressible vortex sheets is studied for
two-dimensional isentropic elastic flows. This problem has a free boundary and
the boundary is characteristic. A necessary and sufficient condition is
obtained for the linear stability of the rectilinear vortex sheets. More
precisely, it is shown that, besides the stable supersonic zone, the elasticity
exerts an additional stable subsonic zone. A new feature for elastic flow is
found that there is a class of states in the interior of subsonic zone where
the stability of such states is weaker than the stability of other states in
the sense that there is an extra loss of tangential derivatives with respect to
the source terms. This is a new feature which Euler flows do not possess. One
of the difficulties for the elastic flow is that the non-differentiable points
of the eigenvalues may coincide with the roots of the Lopatinskii determinant.
As a result, the Kreiss symmetrization cannot be applied directly. Instead, we
perform an upper triangularization of the system to separate only the outgoing
modes at all points in the frequency space, so that an exact estimate of the
outgoing modes can be obtained. Moreover, all the outgoing modes are shown to
be zero due to the $L^2$-regularity of solutions. The estimates for the
incoming modes can be derived directly from the Lopatinskii determinant. This
new approach avoids the lengthy computation and estimates for the outgoing
modes when Kreiss symmetrization is applied. This method can also be applied to
the Euler flows and MHD flows.

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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn