EXISTENCE AND STABILITY OF PERIODIC AND ALMOST PERIODIC SOLUTIONS TO THE BOUSSINESQ SYSTEM IN UNBOUNDED DOMAINS

In this paper we investigate the existence and stability of periodic solutions(on a half-line R+)and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of Rn in the framework of interpolation spaces.For the linear Boussinesq syste...

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Bibliographic Details
Published in:数学物理学报（英文版） 2022, Vol.42 (5), p.1875-1901
Main Authors: Thieu Huy NGUYEN, Truong Xuan PHAM, Thi Ngoc Ha VU, The Sac LE
Format: Article
Language:English
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Summary:In this paper we investigate the existence and stability of periodic solutions(on a half-line R+)and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of Rn in the framework of interpolation spaces.For the linear Boussinesq system we combine the Lp-Lq-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera's principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].
ISSN:0252-9602
DOI:10.3969/j.issn.0252-9602.2022.05.010