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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.

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Acknowledgements

This work was supported by “JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers", Grant Number R2701. Also, the author was supported by JSPS KAKENHI Grant Number JP15H05436.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan

    Ryo Takada

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  1. Ryo Takada
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Correspondence to Ryo Takada.

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Communicated by P. Constantin

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Takada, R. Strongly Stratified Limit for the 3D Inviscid Boussinesq Equations. Arch Rational Mech Anal 232, 1475–1503 (2019). https://doi.org/10.1007/s00205-018-01347-4

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