Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of fully nonlinear KdV-type evolution equations   We study the well-posedness of the initial value problem for fully nonlinear
evolution equations, $u_{t}=f[u],$ where $f$ may depend on up to the first
three spatial derivatives of $u.$ We make three primary assumptions about the
form of $f:$ a regularity assumption, a dispersivity assumption, and an
assumption related to the strength of backwards diffusion. Because the third
derivative of $u$ is present in the right-hand side and we effectively assume
that the equation is dispersive, we say that these fully nonlinear evolution
equations are of KdV-type. We prove the well-posedness of the initial value
problem in the Sobolev space $H^{7}(\mathbb{R}).$ The proof relies on gauged
energy estimates which follow after making two regularizations, a parabolic
regularization and mollification of the initial data.

25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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: math-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics