Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 977-1002 |
| Number of pages | 26 |
| Journal | Journal of Differential Equations |
| Volume | 266 |
| Issue number | 2-3 |
| DOIs | |
| Publication status | Published - Jan 15 2019 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces. / Hieber, Matthias; Mahalov, Alex; Takada, Ryo.
In: Journal of Differential Equations, Vol. 266, No. 2-3, 15.01.2019, p. 977-1002.Research output: Contribution to journal › Article
}
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
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.
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UR - http://www.scopus.com/inward/citedby.url?scp=85051015474&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2018.07.067
DO - 10.1016/j.jde.2018.07.067
M3 - Article
AN - SCOPUS:85051015474
VL - 266
SP - 977
EP - 1002
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2-3
ER -