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June 2022 Cauchy Theory for the Water Waves System in an Analytic Framework
Thomas Alazard, Nicolas Burq, Claude Zuily
Tokyo J. Math. 45(1): 103-199 (June 2022). DOI: 10.3836/tjm/1502179355

Abstract

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 ε in a space of analytic functions which have a holomorphic extension in a strip of size σ, then the solution exists up to a time of size C/ε in a space of analytic functions having at time t a holomorphic extension in a strip of size σCεt.

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Thomas Alazard. Nicolas Burq. Claude Zuily. "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

Information

Received: 21 July 2020; Revised: 28 April 2021; Published: June 2022
First available in Project Euclid: 21 February 2022

Digital Object Identifier: 10.3836/tjm/1502179355

Subjects:
Primary: 35A20
Secondary: 35B65 , 35J25

Keywords: Analytic Sobolev Spaces , Dirichlet-to-Neumann operator , Water-waves

Rights: Copyright © 2022 Publication Committee for the Tokyo Journal of Mathematics

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Vol.45 • No. 1 • June 2022
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