Chemin, Jean-Yves À propos a penalization problem of antisymmetric type. (À propos d’un problème de pénalisation de type antisymétrique.) (French) Zbl 0896.35103 J. Math. Pures Appl., IX. Sér. 76, No. 9, 739-755 (1997). Summary: The author proves that a model of primitive equations of the atmosphere \[ \partial_t v^1+ v\cdot\nabla v^1- \nu\Delta v^1- {1\over\varepsilon} v^2=-{\partial_1\Phi\over \varepsilon},\;\partial_t v^2+ v\cdot\nabla v^2- \nu\Delta v^2+{1\over \varepsilon} v^1=- {\partial_2\Phi\over \varepsilon}, \]\[ \partial_t v^3+ v\cdot\nabla v^3- \nu\Delta v^3+ {1\over\varepsilon} T=- {\partial_3\Phi\over \varepsilon},\;\partial_t T+ v\cdot\nabla T- \nu'\Delta T-{1\over \varepsilon} v^3= 0, \]\[ \text{div }v= 0,\quad (v^1, v^2, v^3, T)|_{t= 0}= (v^1_0, v^2_0, v^3_0, T_0) \] is globally well-posed when it is sufficiently close to the quasi-geostrophic model. Cited in 25 Documents MSC: 35Q30 Navier-Stokes equations 86A05 Hydrology, hydrography, oceanography Keywords:primitive equations of the atmosphere; quasi-geostrophic model PDFBibTeX XMLCite \textit{J.-Y. Chemin}, J. Math. Pures Appl. (9) 76, No. 9, 739--755 (1997; Zbl 0896.35103) Full Text: DOI References: [1] Beale, T.; Bourgeois, A., Validity of the quasi-geostrophic model for large scale flow in the atmosphere and ocean, SIAM Journal of Mathematical Analysis, 25, 1023-1068 (1994) · Zbl 0811.35097 [2] Cannonne, M., Ondelettes, paraproduits et Navier-Stokes, (Diderot Éditeur. Diderot Éditeur, Arts et Sciences (1995)) [3] Chemin, J.-Y., Remarques sur l’existence globale pour le système de Navier-Stokes incompressible, SIAM Journal of Mathematical Analysis, 23, 20-28 (1992) · Zbl 0762.35063 [4] Chemin, J.-Y.; Lerner, N., Flot de champs de vecteurs non-lipschitziens et équations de Navier-Stokes, Journal of Differential Equations, 121, 314-328 (1995) · Zbl 0878.35089 [5] Chemin, J.-Y., Fluides parfaits incompressibles, Astéristique, 230 (1995) · Zbl 0829.76003 [6] Fujita, H.; Kato, T., On the Navier-Stokes initial value problem I, Archiv for Rationnal Mechanic Analysis, 16, 269-315 (1964) · Zbl 0126.42301 [7] Grenier, E., Oscillatory perturbations of the Navier-Stokes equations, (Limite singulière dans les équations de la mécanique des fluides et de la physique des plasmas. Limite singulière dans les équations de la mécanique des fluides et de la physique des plasmas, Thèse de l’Université Paris 6 (1995)) · Zbl 0885.35090 [8] Lions, J.-L., Perturbation singulières dans les problèmes aux limites et en contrôle optimal, (Lecture Notes in Mathematics, 323 (1970), Springer Verlag) · Zbl 0268.49001 [9] J.-L. Lionsprépublication; J.-L. Lionsprépublication [10] Lions, J.-L.; Temam, R.; Wang, S., Geostrophic asympotics of the primitive equations of the atmosphere, Topological Methods in Non Linear Analysis, 4, 1-35 (1994) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.