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Archive for Rational Mechanics and Analysis

, Volume 204, Issue 1, pp 231–271 | Cite as

On the H s Theory of Hydrostatic Euler Equations

Article

Abstract

In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence and uniqueness of H s 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 H s a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity.

Keywords

Vorticity Euler Equation Local Existence Strong Uniqueness Unique Classical Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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