Communications in Mathematical Sciences

Volume 21 (2023)

Number 5

Existence and uniqueness for “good” Boussinesq equations with quasi-periodic initial data

Pages: 1247 – 1278

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n5.a3

Authors

Yixian Gao (School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, Jilin, China)

Yong Li (College of Mathematics, Jilin University, Changchun, Jilin, China; and School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, Jilin, China)

Chang Su (School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China)

Abstract

This paper studies the local well-posedness for the “good” Boussinesq equation subject to quasi-periodic initial conditions. By constructing a delicately and subtly iterative process together with an explicit combinatorial analysis, we show that there exists a unique solution for such a model in a small region of time. The size of this region depends on both the given data and the frequency vector. Moreover the local solution has an expansion with exponentially decaying Fourier coefficients.

Keywords

Boussinesq equations, quasi-periodic initial data, existence, uniqueness, exponential decay

2010 Mathematics Subject Classification

35A01, 35Bxx, 35Q35

Received 8 September 2021

Received revised 1 September 2022

Accepted 16 September 2022

Published 30 August 2023