# American Institute of Mathematical Sciences

March  2013, 12(2): 899-921. doi: 10.3934/cpaa.2013.12.899

## Local well-posedness of quasi-linear systems generalizing KdV

 1 Department of Mathematics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada

Received  September 2011 Revised  August 2012 Published  September 2012

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ödinger 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.
Citation: Timur Akhunov. Local well-posedness of quasi-linear systems generalizing KdV. Communications on Pure & Applied Analysis, 2013, 12 (2) : 899-921. doi: 10.3934/cpaa.2013.12.899
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