Long time solutions for the 2D inviscid Boussinesq equations with strong stratification

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Abstract

We consider the initial value problem of the 2D inviscid Boussinesq equations for stably stratified fluids. We prove the long time existence of classical solutions for large initial data in Hs(R2) with s> 2 when the buoyancy frequency is sufficiently high. Furthermore, we consider the singular limit of the strong stratification, and show that the asymptotic profile of the long time solution is given by the corresponding linear dispersive solution.

Original languageEnglish
JournalManuscripta Mathematica
DOIs
Publication statusAccepted/In press - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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