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Linear Inviscid Damping for Couette Flow in Stratified Fluid

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Abstract

We study the inviscid damping of Couette flow with an exponentially stratified density. The optimal decay rates of the velocity field and the density are obtained for general perturbations with minimal regularity. For Boussinesq approximation model, the decay rates we get are consistent with the previous results in the literature. We also study the decay rates for the full Euler equations of stratified fluids, which were not studied before. For both models, the decay rates depend on the Richardson number in a very similar way. Besides, we also study the dispersive decay due to the exponential stratification when there is no shear.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China

    Jincheng Yang

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332-0160, USA

    Zhiwu Lin

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  1. Jincheng Yang
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  2. Zhiwu Lin
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Correspondence to Zhiwu Lin.

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Communicated by R. Shvydkoy

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Yang, J., Lin, Z. Linear Inviscid Damping for Couette Flow in Stratified Fluid. J. Math. Fluid Mech. 20, 445–472 (2018). https://doi.org/10.1007/s00021-017-0328-3

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  • DOI: https://doi.org/10.1007/s00021-017-0328-3

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