Local Well Posedness of Quasi-Linear Systems Generalizing KdV

2011/10/18 by Timur Akhunov, Akhunov, Timur
Mathematics · Physics and Astronomy · #35G20 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35G20 #msc:35Q53

paper · pdf · doi:10.48550/arxiv.1110.4131

24 pages, to appear in CPAA

arxiv created 2011/10/18 · arxiv updated 2011/10/20

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 Schrödinger 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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