Niveau: Supérieur, Doctorat, Bac+8
Global Existence and Long-Time Asymptotics for Rotating Fluids in a 3D layer Thierry Gallay Institut Fourier (UMR CNRS 5582) Universite de Grenoble I B.P. 74 38402 Saint-Martin-d'Heres, France Violaine Roussier-Michon Institut de Mathematiques de Toulouse (UMR CNRS 5219) INSA Toulouse 135 av Rangueil 31077 Toulouse cedex 4, France December 5, 2008 Abstract The Navier-Stokes-Coriolis system is a simple model for rotating fluids, which allows to study the influence of the Coriolis force on the dynamics of three-dimensional flows. In this paper, we consider the NSC system in an infinite three-dimensional layer delimited by two horizontal planes, with periodic boundary conditions in the vertical direction. If the angular velocity parameter is sufficiently large, depending on the initial data, we prove the existence of global, infinite-energy solutions with nonzero circulation number. We also show that these solutions converge toward two-dimensional Lamb-Oseen vortices as t? ∞. 1
- velocity ?
- u˜ ?
- large initial
- velocity field
- sufficiently large
- nsc system
- dimensional vector
- navier-stokes system
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