Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Hieber, Matthias¹  Mahalov, Alex²  Takada, Ryo³ 

[1] Tech Univ Darmstadt, Fachbereich Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

[2] Arizona State Univ, Sch Math & Stat Sci, POB 871804, Tempe, AZ 85287 USA

[3] Kyushu Univ, Fac Math, Fukuoka, Fukuoka 8190395, Japan

关键词: Time periodic solutions;    Almost time periodic solutions;    Rotating stably stratified fluids;    Dispersive estimates;   

DOI  :  10.1016/j.jde.2018.07.067

来源: Elsevier

【 摘 要 】

Consider the 3D incompressible Boussinesq equations for rotating stably stratified fluids. It is shown that this set of equations possesses a unique time periodic or almost time periodic solutions for external forces satisfying these properties, which, however, do not necessarily need to be small. An explicit bound on the size of the external force, depending on the buoyancy frequency N, is given, which then allows for the unique existence of time periodic or almost periodic solutions. In particular, the size of the external forces can be taken large with respect to the buoyancy frequency. The approach depends crucially on the dispersive effect of the rotation and the stable stratification. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free