Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of the water-wave with viscosity problem   In this paper we study the motion of a surface gravity wave with viscosity.
In particular we prove two well-posedness results. On the one hand, we
establish the local solvability in Sobolev spaces for arbitrary dissipation. On
the other hand, we establish the global well-posedness in Wiener spaces for a
sufficiently large viscosity. These results are the first rigorous proofs of
well-posedness for the Dias, Dyachenko \& Zakharov system ({\em Physics Letters
A} 2008) modelling gravity waves with viscosity when surface tension is not
taken into account.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an