Existence of a solution ‘in the large’ for the 3D large-scale ocean dynamics equations

Georgij M. Kobelkov

doi:10.1016/j.crma.2006.04.020

Numerical Analysis

Existence of a solution ‘in the large’ for the 3D large-scale ocean dynamics equations
[L'existence d'une solution en 3D pour la dynamique de l'océan à grande échelle]

Présenté par : Olivier Pironneau

Georgij M. Kobelkov ¹

¹ Department of Mechanics and Mathematics of Moscow State University, Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

Comptes Rendus. Mathématique, Volume 343 (2006) no. 4, pp. 283-286.

Résumé
Abstract

L'auteur considère le système 3D d'équations décrivant la dynamique de l'océan à grande échelle en coordonnées cartésiennes. Il démontre, pour tout coefficient de viscosité et toute donnée initiale, l'existence et l'unicité d'une solution sur un intervalle de temps $[0, T]$ arbitrairement, ainsi que la continuité en temps sur l'intervalle $[0, T]$ de la norme $‖ {\hat{u}}_{x} ‖$ .

For the 3D system of equations describing large-scale ocean dynamics in the Cartesian coordinate system existence and uniqueness of a solution on an arbitrary time interval $[0, T]$ is proved and the norm $‖ {\hat{u}}_{x} ‖$ is shown to be continuous in time on $[0, T]$ .

Reçu le : 2005-11-01
Accepté le : 2006-03-30
Publié le : 2006-07-14

DOI : 10.1016/j.crma.2006.04.020

Affiliations des auteurs :

Georgij M. Kobelkov ¹

¹ Department of Mechanics and Mathematics of Moscow State University, Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

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     title = {Existence of a solution {\textquoteleft}in the large{\textquoteright} for the {3D} large-scale ocean dynamics equations},
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     pages = {283--286},
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Georgij M. Kobelkov. Existence of a solution ‘in the large’ for the 3D large-scale ocean dynamics equations. Comptes Rendus. Mathématique, Volume 343 (2006) no. 4, pp. 283-286. doi : 10.1016/j.crma.2006.04.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.020/

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