Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of the free-boundary compressible 3-D Euler equations
  with surface tension and the zero surface tension limit   We prove that the 3-D compressible Euler equations with surface tension along
the moving free-boundary are well-posed. Specifically, we consider isentropic
dynamics and consider an equation of state, modeling a liquid, given by Courant
and Friedrichs as $p(\rho) = \alpha \rho^ \gamma - \beta$ for consants $\gamma
>1$ and $ \alpha, \beta > 0$. The analysis is made difficult by two competing
nonlinearities associated with the potential energy: compression in the bulk,
and surface area dynamics on the free-boundary. Unlike the analysis of the
incompressible Euler equations, wherein boundary regularity controls regularity
in the interior, the compressible Euler equation require the additional
analysis of nonlinear wave equations generating sound waves. An existence
theory is developed by a specially chosen parabolic regularization together
with the vanishing viscosity method. The artificial parabolic term is chosen so
as to be asymptotically consistent with the Euler equations in the limit of
zero viscosity. Having solutions for the positive surface tension problem, we
proceed to obtain a priori estimates which are independent of the surface
tension parameter. This requires choosing initial data which satisfy the Taylor
sign condition. By passing to the limit of zero surface tension, we prove the
well-posedness of the compressible Euler system without surface on the
free-boundary, and without derivative loss.

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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn