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arXiv · 1110.4131

Local Well Posedness of Quasi-Linear Systems Generalizing KdV

Timur Akhunov
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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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Timur Akhunov. 2011-10-18. Local Well Posedness of Quasi-Linear Systems Generalizing KdV. https://arxiv.org/abs/1110.4131

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