### Abstract

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 language | English (US) |
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Pages (from-to) | 375-394 |

Number of pages | 20 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 142 |

Issue number | 4 |

Publication status | Published - Aug 30 1998 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mathematics(all)
- Mathematics (miscellaneous)