The Euler limit of the Navier-Stokes equations, and rotating fluids with boundary

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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.

Original languageEnglish (US)
Pages (from-to)375-394
Number of pages20
JournalArchive for Rational Mechanics and Analysis
Issue number4
StatePublished - Aug 30 1998


ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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