Abstract

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 languageEnglish (US)
Pages (from-to)691-706
Number of pages16
JournalBulletin of the London Mathematical Society
Volume42
Issue number4
DOIs
StatePublished - Aug 2010

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Nonlinear Stability
Boundary Layer
Stationary Solutions
Decay Rate
Half-space
Dirichlet Boundary Conditions
Reynolds number
Initial Value Problem
Navier-Stokes Equations
Decay
Perturbation
Three-dimensional

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonlinear stability of Ekman boundary layers. / Hess, Matthias; Hieber, Matthias; Mahalov, Alex; Saal, Jürgen.

In: Bulletin of the London Mathematical Society, Vol. 42, No. 4, 08.2010, p. 691-706.

Research output: Contribution to journalArticle

Hess, Matthias ; Hieber, Matthias ; Mahalov, Alex ; Saal, Jürgen. / Nonlinear stability of Ekman boundary layers. In: Bulletin of the London Mathematical Society. 2010 ; Vol. 42, No. 4. pp. 691-706.
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