Low regularity well-posedness for two-dimensional deep water waves
Abstract
The study of gravity-capillary water waves in two space dimensions has been an important question in mathematical fluid dynamics. By implementing the cubic modified energy method of Ifrim-Tataru in the context of gravity-capillary waves, we show that for s> 1, the two-dimensional gravity-capillary water wave system is locally well-posed in Hs.
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