Strongly Stratified Limit for the 3D Inviscid Boussinesq Equations

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Abstract

We consider the initial value problem of the 3D inviscid Boussinesq equations for stably stratified fluids. We prove the long time existence of classical solutions for large initial data when the buoyancy frequency is sufficiently high. Furthermore, we consider the singular limit of the strong stratification, and show that the long time classical solution converges to that of 2D incompressible Euler equations in some space-time Strichartz norms.

Original languageEnglish
Pages (from-to)1475-1503
Number of pages29
JournalArchive for Rational Mechanics and Analysis
Volume232
Issue number3
DOIs
Publication statusPublished - Jun 3 2019

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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