Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anisotropic decay and global well-posedness of viscous surface waves
  without surface tension   We consider a viscous incompressible fluid below the air and above a fixed
bottom. The fluid dynamics is governed by the gravity-driven incompressible
Navier-Stokes equations, and the effect of surface tension is neglected on the
free surface. The global well-posedness and long-time behavior of solutions
near equilibrium have been intriguing questions since Beale (\emph{Comm. Pure
Appl. Math.} 34 (1981), no. 3, 359--392). It had been thought that certain low
frequency assumption of the initial data is needed to derive an integrable
decay rate of the velocity so that the global solutions in $3D$ can be
constructed, while the global well-posedness in $2D$ was left open. In this
paper, by exploiting the anisotropic decay rates of the velocity, which are
even not integrable, we prove the global well-posedness in both $2D$ and $3D$,
without any low frequency assumption of the initial data. One of key
observations here is a cancelation in nonlinear estimates of the viscous stress
tensor term in the bulk by using Alinhac good unknowns, when estimating the
energy evolution of the highest order horizontal spatial derivatives of the
solution.

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The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg