Local well-posedness of quasi-linear systems generalizing KdV
Timur Akhunov
Communications on Pure & Applied Analysis 2013, 12(2): 899-921 doi: 10.3934/cpaa.2013.12.899
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.
keywords: energy method. quasilinear KdV dispersive partial differential equations

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