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

Matthias Georg Hieber, Alex Mahalov, Ryo Takada

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1 Citation (Scopus)

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 languageEnglish
JournalJournal of Differential Equations
DOIs
Publication statusAccepted/In press - 2018 Jan 1
Externally publishedYes

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Keywords

  • Almost time periodic solutions
  • Dispersive estimates
  • Rotating stably stratified fluids
  • Time periodic solutions

ASJC Scopus subject areas

  • Analysis

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