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Global well-posedness for the primitive equations with less regular initial data
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 17 (2008) no. 2, pp. 221-238.

Cet article est consacré à l’étude du temps d’existence des solutions du système des équations primitives pour des données moins régulières. On interpole les résultats d’existence globale à données H ˙ 1 2 petites fournis par le théorème de Fujita-Kato, et le résultat de [6] qui donne l’existence globale si le paramètre de Rossby ε est suffisamment petit, et pour des données plus régulières (partie oscillante initiale dans H ˙ 1 2 H ˙ 1 et partie quasigéostrophique initiale dans H 1 )

This paper is devoted to the study of the lifespan of the solutions of the primitive equations for less regular initial data. We interpolate the globall well-posedness results for small initial data in H ˙ 1 2 given by the Fujita-Kato theorem, and the result from [6] which gives global well-posedness if the Rossby parameter ε is small enough, and for regular initial data (oscillating part in H ˙ 1 2 H ˙ 1 and quasigeostrophic part in H 1 ).

Reçu le : 2006-02-28
Accepté le : 2007-10-14
Publié le : 2008-12-11
DOI : https://doi.org/10.5802/afst.1182
@article{AFST_2008_6_17_2_221_0,
     author = {Fr\'ed\'eric Charve},
     title = {Global well-posedness for the primitive equations with less regular initial data},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {221--238},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 17},
     number = {2},
     year = {2008},
     doi = {10.5802/afst.1182},
     zbl = {1160.35301},
     mrnumber = {2487854},
     language = {en},
     url = {afst.centre-mersenne.org/item/AFST_2008_6_17_2_221_0/}
}
Frédéric Charve. Global well-posedness for the primitive equations with less regular initial data. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 17 (2008) no. 2, pp. 221-238. doi : 10.5802/afst.1182. https://afst.centre-mersenne.org/item/AFST_2008_6_17_2_221_0/

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