Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Wellposedness of Viscous Surface Wave without Surface Tension   We consider an incompressible viscous flow without surface tension in a
finite- depth domain of three dimension, with free top boundary. This system is
governed by a Naiver-Stokes equation in a moving domain and a transport
equation for the top boundary. Traditionally, we consider this problem in
Lagrangian coordinate and perturbed linear form. In [1], I. Tice and Y. Guo
introduced a new framework using geometric structure in Eulerian coordinate to
study both local and global wellposedness of this system. Following this path,
we extend their result in local wellposedness from small data case to arbitrary
data case. Other than the geometric energy estimate and time-dependent Galerkin
method introduced in [1], we utilize a few new techniques: (1) using
parameterized Poisson integral to construct a nontrivial transform between
fixed domain and moving domain; (2) using bootstrapping argument to prove a
comparison result for steady Navier-Stokes equation for arbitrary data of free
surface.

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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int