Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes
  Equations with Surface Tension   The two-phase free boundary value problem for the isothermal Navier-Stokes
system is studied for general bounded geometries in absence of phase
transitions, external forces and boundary contacts. It is shown that the
problem is well-posed in an Lp-setting, and that it generates a local semiflow
on the induced phase manifold. If the phases are connected, the set of
equilibria of the system forms a (n+1)-dimensional manifold, each equilibrium
is stable, and it is shown that global solutions which do not develop
singularities converge to an equilibrium as time goes to infinity. The latter
is proved by means of the energy functional combined with the generalized
principle of linearized stability.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th