Dispersive estimates for the stably stratified boussinesq equations

Sanghyuk Lee, Ryo Takada

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We consider the initial value problem for the 3D Boussinesq equations for stably stratified fluids without the rotational effect. We establish the sharp dispersive estimate for the linear propagator related to the stable stratification. As an application, we give the explicit relation between the size of initial data and the buoyancy frequency which ensures the unique existence of global solutions to our system. In particular, it is shown that the size of the initial thermal disturbance can be taken in proportion to the strength of stratification.

Original languageEnglish
Pages (from-to)2037-2070
Number of pages34
JournalIndiana University Mathematics Journal
Issue number6
Publication statusPublished - 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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