Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-decay estimates for linearized two-phase Navier-Stokes equations
  with surface tension and gravity   The aim of this paper is to show time-decay estimates of solutions to
linearized two-phase Navier-Stokes equations with surface tension and gravity.
The original two-phase Navier-Stokes equations describe the two-phase
incompressible viscous flow with a sharp interface that is close to the
hyperplane $x_N=0$ in the $N$-dimensional Euclidean space, $N \geq 2$. It is
well-known that the Rayleigh-Taylor instability occurs when the upper fluid is
heavier than the lower one, while this paper assumes that the lower fluid is
heavier than the upper one and proves time-decay estimates of $L_p-L_q$ type
for the linearized equations. Our approach is based on solution formulas, given
by Shibata and Shimizu (2011), for a resolvent problem associated with the
linearized equations.

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The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
25
The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph