Analysis Seminar

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Global well-posedness for non-localized 3D gravity water waves

Speaker: Benjamin Pineau, NYU

Location: Warren Weaver Hall 1302

Date: Thursday, April 23, 2026, 11 a.m.

Synopsis:

I will describe a work in progress on the problem of well-posedness for small data in $H^s$ based (i.e. non-localized) Sobolev spaces for gravity water waves in a fluid of infinite depth in spatial dimension $d\geq 3$ and higher. Our main result establishes global well-posedness in low regularity, non-localized $H^s$ based Sobolev spaces assuming only smallness of the data in a critical Sobolev (more precisely, Besov) norm. All previous global well-posedness results required the data to be localized and much more regular. This is joint work with Mihaela Ifrim and Daniel Tataru.