Archive for Rational Mechanics and Analysis

, Volume 142, Issue 4, pp 375–394 | Cite as

The Euler Limit of the Navier‐Stokes Equations, and Rotating Fluids with Boundary

  • Nader Masmoudi


In this paper we study the convergence of weak solutions of the Navier-Stokes equations in some particular domains, with different horizontal and vertical viscosities, when they go to zero with different speeds. The difficulty here comes from the Dirichlet boundary conditions. Precisely we show that if the ratio of the vertical viscosity to the horizontal viscosity also goes to zero, then the solutions converge to the solution of the Euler system. We study the same limit for rotating fluids with Rossby number also going to zero.


Viscosity Boundary Condition Weak Solution Dirichlet Boundary Dirichlet Boundary Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Nader Masmoudi
    • 1
  1. 1.Département de Mathématiques et d'Informatique, École Normale Supérieure, 45 rue d'Ulm, 75005 Paris, FranceFR

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