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

作　　者：Thieu Huy NGUYEN Truong Xuan PHAM Thi Ngoc Ha VU The Sac LE 

机构地区：[1]School of Applied Mathematics and Informatics,Hanoi University of Science and Technology Vien Toan ung dung va Tin hoc,Dai hoc Bach khoa Hanoi 1DaiCoViet,Hanoi,Vietnam [2]Department of Mathematics,Faculty of Information Technology,Thuyloi university Khoa Cong nghe Thong tin,Bo mon Toan,Dai hoc Thuy loi,175 Tay Son,Dong Da,Ha Noi,Viet Nam [3]Thuyloi University,Dai hoc Thuy Loi,175 Tay Son,Dong Da,Hanoi,Viet Nam

出　　处：《Acta Mathematica Scientia》2022年第5期1875-1901,共27页数学物理学报（B辑英文版）

基　　金：financially supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.02-2021.04;financially supported by Vietnam Ministry of Education and Training under Project B2022-BKA-06.

摘　　要：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 R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-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].

关 键 词：Boussinesq systems periodic solutions almost periodic solutions unbounded domains smoothing estimates dual estimates interpolation spaces STABILITY 

分 类 号：O175[理学—数学]