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Analytic Solutions For The Water-Waves System

[Moved Online] Recent Developments in Fluid Dynamics April 12, 2021 - April 30, 2021

April 16, 2021 (09:00 AM PDT - 09:50 AM PDT)
Speaker(s): Nicolas Burq (Université de Paris XI)
Location: MSRI: Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Analytic Cauchy Theory for the Gravity Water-Wave System

Abstract

In  this talk I will present some results on  the Cauchy problem for the gravity water-wave equations, in a domain with flat bottom and in arbitrary space dimension. I will show that if the data are of size $\eps$ in a space of analytic functions which have a holomorphic extension in a strip of size $\sigma$, then the solution exists up to a time of size $C/\eps$ in a space of analytic functions having at time $t$ a holomorphic extension in a strip of size $\sigma - C'\eps t$. This question comes from motivations from control theory which force us to consider analytic solutions. I will actually start the talk with these motivations.

This is joint work with T. Alazard and C. Zuily.