TY - JOUR
T1 - Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces
AU - Hieber, Matthias
AU - Mahalov, Alex
AU - Takada, Ryo
N1 - Funding Information:
This work was supported by “ JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers”, Grant Number R2701 . A. Mahalov was partially supported by NSF Grant Number DMS 1419593 . R. Takada was partially supported by JSPS KAKENHI Grant Number JP15H05436 .
Funding Information:
This work was supported by “JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers”, Grant Number R2701. A. Mahalov was partially supported by NSF Grant Number DMS 1419593. R. Takada was partially supported by JSPS KAKENHI Grant Number JP15H05436.
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/1/15
Y1 - 2019/1/15
N2 - 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.
AB - 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.
KW - Almost time periodic solutions
KW - Dispersive estimates
KW - Rotating stably stratified fluids
KW - Time periodic solutions
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U2 - 10.1016/j.jde.2018.07.067
DO - 10.1016/j.jde.2018.07.067
M3 - Article
AN - SCOPUS:85051015474
SN - 0022-0396
VL - 266
SP - 977
EP - 1002
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2-3
ER -