Nonlinear stability of Ekman boundary layers

Matthias Hess, Matthias Georg Hieber, Alex Mahalov, Jürgen Saal

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9 Citations (Scopus)

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
Pages (from-to)691-706
Number of pages16
JournalBulletin of the London Mathematical Society
Volume42
Issue number4
DOIs
Publication statusPublished - 2010 Aug
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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