### 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 L^{2}-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) |
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Pages (from-to) | 691-706 |

Number of pages | 16 |

Journal | Bulletin of the London Mathematical Society |

Volume | 42 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2010 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the London Mathematical Society*,

*42*(4), 691-706. https://doi.org/10.1112/blms/bdq029

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

Research output: Contribution to journal › Article

*Bulletin of the London Mathematical Society*, vol. 42, no. 4, pp. 691-706. https://doi.org/10.1112/blms/bdq029

}

TY - JOUR

T1 - Nonlinear stability of Ekman boundary layers

AU - Hess, Matthias

AU - Hieber, Matthias

AU - Mahalov, Alex

AU - Saal, Jürgen

PY - 2010/8

Y1 - 2010/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77954829671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954829671&partnerID=8YFLogxK

U2 - 10.1112/blms/bdq029

DO - 10.1112/blms/bdq029

M3 - Article

AN - SCOPUS:77954829671

VL - 42

SP - 691

EP - 706

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 4

ER -