Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 2, pp 445–472 | Cite as

Linear Inviscid Damping for Couette Flow in Stratified Fluid

  • Jincheng Yang
  • Zhiwu Lin


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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© Springer International Publishing 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlanta, GeorgiaUSA

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