no. 9
Sur les équations α Navier–Stokes dans un ouvert borné
Valentina Busuioc, Adriana1
1 Département de mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Suisse
Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 823-826

On considère les équations α Navier–Stokes (LANS-α) dans un domaine borné de ℝ 3 . On montre l'existence et l'unicité globale des solutions, en supposant que la donnée initiale appartient à H10.

We consider the Lagrangian averaged Navier–Stokes (LANS-α) equations in a bounded domain of ℝ 3 . We prove global existence and uniqueness of solutions under the hypothesis that the initial data belongs to H10.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02369-5

Valentina Busuioc, Adriana 1

1 Département de mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Suisse 
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Valentina Busuioc, Adriana. Sur les équations $ \mathbf{\alpha }$ Navier–Stokes dans un ouvert borné. Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 823-826. doi: 10.1016/S1631-073X(02)02369-5

[1] Valentina Busuioc, A. On second grade fluids with vanishing viscosity, C. R. Acad. Sci. Paris, Série I, Volume 328 (1999) no. 12, pp. 1241-1246

[2] Camassa, R.; Holm, D.D. An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., Volume 71 (1993) no. 11, pp. 1661-1664

[3] Chen, S.; Foias, C.; Holm, D.D.; Olson, E.; Titi, E.S.; Wynne, S. The Camassa–Holm equations as a closure model for turbulent channel and pipe flow, Phys. Rev. Lett., Volume 81 (1998), pp. 5338-5341

[4] Cioranescu, D.; Ouazar, E.H. Existence and uniqueness for fluids of second grade, Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. VI, Paris, 1982/1983, Pitman, Boston, MA, 1984, pp. 178-197

[5] D. Coutand, J. Peirce, S. Shkoller, Global well-posedness of weak solutions for the Lagrangian averaged Navier–Stokes equations on bounded domains, Comm. Pure Appl. Anal., to appear

[6] C. Foias, D.D. Holm, E.S. Titi, The three-dimensional viscous Camassa–Holm equations and their relation to the Navier–Stokes equation and turbulence theory, J. Dynamics Differential Equations, to appear

[7] Holm, D.D.; Marsden, J.E.; Ratiu, T. Euler–Poincaré models of ideal fluids with nonlinear dispersion, Phys. Rev. Lett., Volume 80 (1998) no. 19, pp. 4173-4177

[8] Kouranbaeva, S. The Camassa–Holm equation as a geodesic flow on the diffeomorphism group, J. Math. Phys., Volume 40 (1999) no. 2, pp. 857-868

[9] Marsden, J.E.; Shkoller, S. Global well-posedness for the LANS-α equations on bounded domains, Philos. Trans. Roy. Soc. London Ser. A, Volume 359 (2001), pp. 1449-1468

[10] Misiolek, G. A shallow water equation as a geodesic flow on the Bott–Virasoro group, J. Geom. Phys., Volume 24 (1998) no. 3, pp. 203-208

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