Global existence and long-time asymptotics for rotating fluids in a 3D layer |
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Authors: | Thierry Gallay Violaine Roussier-Michon |
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Institution: | aInstitut Fourier (UMR CNRS 5582), Université de Grenoble I, B.P. 74, 38402 Saint-Martin-d'Hères, France;bInstitut de Mathématiques de Toulouse (UMR CNRS 5219), INSA Toulouse, 135 av Rangueil, 31077 Toulouse cedex 4, France |
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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→∞. |
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Keywords: | Navier– Stokes equation Rotating fluids Global existence Long-time asymptotics Three-dimensional layer Oseen vortex |
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