Local Well Posedness of Quasi-Linear Systems Generalizing KdV
Analysis of PDEs
2011-10-20 v1 Mathematical Physics
math.MP
Abstract
In this article we prove local well-posedness of quasilinear dispersive systems of PDE generalizing KdV. These results adapt the ideas of Kenig- Ponce-Vega from the Quasi-Linear Schr\"odinger equations to the third order dispersive problems. The main ingredient of the proof is a local smoothing estimate for a general linear problem that allows us to proceed via the artificial viscosity method.
Keywords
Cite
@article{arxiv.1110.4131,
title = {Local Well Posedness of Quasi-Linear Systems Generalizing KdV},
author = {Timur Akhunov},
journal= {arXiv preprint arXiv:1110.4131},
year = {2011}
}
Comments
24 pages, to appear in CPAA