Nous donnons un résultat d'existence et d'unicité de la solution faible-renormalisée d'un système non linéaire de Boussinesq. On établit des résultats de régularité pour l'équation de la chaleur que l'on combine avec les techniques usuelles pour les équations de Navier–Stokes et celles des solutions renormalisées pour des problèmes paraboliques.
We give existence and uniqueness results of the weak-renormalized solution for a class of nonlinear Boussinesq systems. We establish regularity results for the heat equation which we combine with the usual techniques for Navier–Stokes equations mixed with the tools involved for renormalized solutions.
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@article{CRMATH_2008__346_9-10_521_0,
author = {Bruy\`ere, Nicolas},
title = {Existence et unicit\'e de la solutions faible-renormalis\'ee pour un syst\`eme non lin\'eaire de {Boussinesq}},
journal = {Comptes Rendus. Math\'ematique},
pages = {521--526},
publisher = {Elsevier},
volume = {346},
number = {9-10},
year = {2008},
doi = {10.1016/j.crma.2008.03.005},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.03.005/}
}
TY - JOUR AU - Bruyère, Nicolas TI - Existence et unicité de la solutions faible-renormalisée pour un système non linéaire de Boussinesq JO - Comptes Rendus. Mathématique PY - 2008 SP - 521 EP - 526 VL - 346 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.03.005/ DO - 10.1016/j.crma.2008.03.005 LA - fr ID - CRMATH_2008__346_9-10_521_0 ER -
%0 Journal Article %A Bruyère, Nicolas %T Existence et unicité de la solutions faible-renormalisée pour un système non linéaire de Boussinesq %J Comptes Rendus. Mathématique %D 2008 %P 521-526 %V 346 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.03.005/ %R 10.1016/j.crma.2008.03.005 %G fr %F CRMATH_2008__346_9-10_521_0
Bruyère, Nicolas. Existence et unicité de la solutions faible-renormalisée pour un système non linéaire de Boussinesq. Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 521-526. doi : 10.1016/j.crma.2008.03.005. http://www.numdam.org/articles/10.1016/j.crma.2008.03.005/
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