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À propos a penalization problem of antisymmetric type. (À propos d’un problème de pénalisation de type antisymétrique.) (French) Zbl 0896.35103

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.

MSC:

35Q30 Navier-Stokes equations
86A05 Hydrology, hydrography, oceanography
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