English

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