Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Nash-Moser theorem for singular evolution equations. Application to
  the Serre and Green-Naghdi equations   We study the well-posedness of the initial value problem for a wide class of
singular evolution equations. We prove a general well-posedness theorem under
three assumptions easy to check: the first controls the singular part of the
equation, the second the behavior of the nonlinearities, and the third one
assumes that an energy estimate can be found for the linearized system. We
allow losses of derivatives in this energy estimate and therefore construct a
solution by a Nash-Moser iterative scheme. As an application to this general
theorem, we prove the well-posedness of the Serre and Green-Naghdi equation and
discuss the problem of their validity as asymptotic models for the water-waves
equations.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an