Communications in Mathematical Sciences
Volume 21 (2023)
Existence and uniqueness for “good” Boussinesq equations with quasi-periodic initial data
Pages: 1247 – 1278
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.
Boussinesq equations, quasi-periodic initial data, existence, uniqueness, exponential decay
2010 Mathematics Subject Classification
35A01, 35Bxx, 35Q35
The research of Y.G. was supported by NSFC grants 11871140, 12071065 and FRFCU2412019BJ005.
The research of Y.L. was supported in part by NSFC grant 12071175.
Received 8 September 2021
Received revised 1 September 2022
Accepted 16 September 2022
Published 30 August 2023