Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sharp stability criterion for propagating phase boundaries in
  Korteweg's model   Recently, Benzoni--Gavage, Danchin, Descombes, and Jamet have given a
sufficient condition for linear and nonlinear stability of solitary wave
solutions of Korteweg's model for phase-transitional isentropic gas dynamics in
terms of convexity of a certain ``moment of instability'' with respect to wave
speed, which is equivalent to variational stability with respect to the
associated Hamiltonian energy under a partial subset of the constraints of
motion; they conjecture that this condition is also necessary. Here, we compute
a sharp criterion for spectral stability in terms of the second derivative of
the Evans function at the origin, and show that it is equivalent to the
variational condition obtained by Benzoni--Gavage et al, answering their
conjecture in the positive.

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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
18
The categories of this paper are: econ