The initial value problem for a third order dispersive equation on the two-dimensional torus
Analysis of PDEs
2007-05-23 v2 Classical Analysis and ODEs
Abstract
We present the necessary and sufficient condition for the -well-posedness of the initial problem for a third order linear dispersive equation on the two dimensional torus. Birkhoff's method of asymptotic solutions is used to prove the necessity. Some properties of a system for quadratic algebraic equations associated to the principal symbol play crucial role in proving the sufficiency.
Cite
@article{arxiv.math/0404006,
title = {The initial value problem for a third order dispersive equation on the two-dimensional torus},
author = {Hiroyuki Chihara},
journal= {arXiv preprint arXiv:math/0404006},
year = {2007}
}
Comments
7 pages, no figure