Archive for Rational Mechanics and Analysis

, Volume 204, Issue 1, pp 231–271

On the Hs Theory of Hydrostatic Euler Equations



In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence and uniqueness of Hs solutions under the local Rayleigh condition. This extends Brenier’s (Nonlinearity 12(3):495–512, 1999) existence result by removing an artificial condition and proving uniqueness. In addition, we prove weak–strong uniqueness, mathematical justification of the formal derivation and stability of the hydrostatic Euler equations. These results are based on weighted Hs a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Courant InstituteNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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