Geodesic
Une perturbation hyperbolique des équations de Navier-Stokes
Marius Paicu1 ; Geneviève Raugel2
1 Univ Paris-Sud, Laboratoire de Mathématiques d'Orsay, Orsay Cedex, F-91405; CNRS, Orsay cedex, F-91405
2 CNRS, Laboratoire de Mathématiques d'Orsay, Orsay Cedex, F-91405; Univ Paris-Sud, Orsay cedex, F-91405
ESAIM. Proceedings, Tome 21 (2007), pp. 65-87.

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In this paper, we consider a hyperbolic perturbation of the Navier-Stokes equations in , n=2,3, given by (0.2), which consists in adding the term to the Navier-Stokes equations. In the case n=2, we recall the global existence and uniqueness of mild solutions of (0.2), for initial data in the Hilbert space and appropriate forcing term f, when is small enough, that has been proved in [16]. In the three-dimensional case, we prove a global existence result under a smallness condition of the initial data in , , for an appropriate forcing term f, when is small enough. This smallness condition is analogous to the one known for the global existence of strong solutions of the three-dimensional Navier-Stokes equations.
DOI : 10.1051/proc:072106

Marius Paicu 1 ; Geneviève Raugel 2

1 Univ Paris-Sud, Laboratoire de Mathématiques d'Orsay, Orsay Cedex, F-91405; CNRS, Orsay cedex, F-91405
2 CNRS, Laboratoire de Mathématiques d'Orsay, Orsay Cedex, F-91405; Univ Paris-Sud, Orsay cedex, F-91405 
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     author = {Marius Paicu and Genevi\`eve Raugel},
     title = {Une perturbation hyperbolique des \'equations de {Navier-Stokes}},
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Marius Paicu; Geneviève Raugel. Une perturbation hyperbolique des équations de Navier-Stokes. ESAIM. Proceedings, Tome 21 (2007), pp. 65-87. doi : 10.1051/proc:072106. http://geodesic.mathdoc.fr/articles/10.1051/proc:072106/

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