Consider the initial value problem for the three-dimensional Navier-Stokes equations with rotation in the half-space 3+ subject to Dirichlet boundary conditions as well as the Ekman spiral, which is a stationary solution to the above equations. It is proved that the Ekman spiral is nonlinearly stable with respect to L2-perturbations provided that the corresponding Reynolds number is small enough. Moreover, the decay rate can be computed in terms of the decay of the corresponding linear problem.
|Original language||English (US)|
|Number of pages||16|
|Journal||Bulletin of the London Mathematical Society|
|State||Published - Aug 2010|
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