Advances in Differential Equations

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

Thierry Colin and Pierre Fabrie

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 22 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366638964

Mathematical Reviews number (MathSciNet)
MR1751425

Zentralblatt MATH identifier
1023.76593

Subjects
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

Citation

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. https://projecteuclid.org/euclid.ade/1366638964


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