The initial value problem for a third order dispersive equation on the two-dimensional torus
Abstract
We present the necessary and sufficient condition for the $L^2$-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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- April 2004
- DOI:
- 10.48550/arXiv.math/0404006
- arXiv:
- arXiv:math/0404006
- Bibcode:
- 2004math......4006C
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Classical Analysis and ODEs;
- 35G10
- E-Print:
- 7 pages, no figure