Large data local well-posedness for a class of KdV-type equations
Analysis of PDEs
2013-06-26 v3
Abstract
In this article we consider the Cauchy problem with large initial data for an equation of the form (\partial_t+\partial_x^3)u=F(u,u_x,u_{xx}) where F is a polynomial with no constant or linear terms. Local well-posedness was established in weighted Sobolev spaces by Kenig-Ponce-Vega. In this paper we prove local well-posedness in a translation invariant subspace of H^s by adapting the result of Marzuola-Metcalfe-Tataru on quasilinear Schrodinger equations.
Keywords
Cite
@article{arxiv.1110.5402,
title = {Large data local well-posedness for a class of KdV-type equations},
author = {Benjamin Harrop-Griffiths},
journal= {arXiv preprint arXiv:1110.5402},
year = {2013}
}
Comments
21 pages. Some typos corrected, references updated