The initial value problem for a third order dispersive equation on the twodimensional torus
Abstract
We present the necessary and sufficient condition for the $L^2$wellposedness 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404006
 Bibcode:
 2004math......4006C
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Classical Analysis and ODEs;
 35G10
 EPrint:
 7 pages, no figure