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.
Citation
Thierry Colin. Pierre Fabrie. "Rotating fluid at high Rossby number driven by a surface stress: existence and convergence." Adv. Differential Equations 2 (5) 715 - 751, 1997. https://doi.org/10.57262/ade/1366638964
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