In this paper we consider the Cauchy problem for the gravity water-wave equations, in a domain with flat bottom and in arbitrary space dimension. We prove that if the data are of size in a space of analytic functions which have a holomorphic extension in a strip of size , then the solution exists up to a time of size in a space of analytic functions having at time a holomorphic extension in a strip of size .
"Cauchy Theory for the Water Waves System in an Analytic Framework." Tokyo J. Math. 45 (1) 103 - 199, June 2022. https://doi.org/10.3836/tjm/1502179355