Advances in Differential Equations

Rotating fluid at high Rossby number driven by a surface stress: existence and convergence

Thierry Colin and Pierre Fabrie

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We consider the 3-D Navier-Stokes equations with Coriolis force of order $\frac{1}{\epsilon}$ and vanishing vertical viscosity of order $\epsilon$. For suitable initial data, we prove some long-time existence results. Moreover, we obtain convergence as $\epsilon$ goes to 0 to the 2-D Navier-Stokes equations. We deal with periodic boundary conditions and nonhomogeneous stress. In this case, we compute and justify the corrector.

Article information

Adv. Differential Equations, Volume 2, Number 5 (1997), 715-751.

First available in Project Euclid: 22 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76U05: Rotating fluids
Secondary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30] 76D10: Boundary-layer theory, separation and reattachment, higher-order effects


Colin, Thierry; Fabrie, Pierre. Rotating fluid at high Rossby number driven by a surface stress: existence and convergence. Adv. Differential Equations 2 (1997), no. 5, 715--751.

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