Local Well Posedness of Quasi-Linear Systems Generalizing KdV

Details Local Well Posedness of Quasi-Linear Systems Generalizing KdV Local Well Posedness of Quasi-Linear Systems Generalizing KdV

2011-10-18

arxiv.org/abs/1110.4131v1

Mathematics

Analysis of PDEs

24 pages, to appear in CPAA

Scientific paper

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.

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