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Low regularity Cauchy theory for the water-waves problem: canals and swimming pools

T. AlazardN. BurqC. Zuily — 2011

Journées Équations aux dérivées partielles

The purpose of this talk is to present some recent results about the Cauchy theory of the gravity water waves equations (without surface tension). In particular, we clarify the theory as well in terms of regularity indexes for the initial conditions as fin terms of smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developed in [, ], after suitable para-linearizations, the system can be arranged into...

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