28 articles  [english version]
 HAL : hal-00464890, version 2
 arXiv : 1003.4921
 Versions disponibles : v2 (28-07-2010)
 Large time decay and growth for solutions of a viscous Boussinesq system
 (18/03/2010)
 In this paper we analyze the decay and the growth for large time of weak and strong solutions to the three-dimensional viscous Boussinesq system. We show that generic solutions blow up as $t\to\infty$ in the sense that the energy and the $L^p$-norms of the velocity field grow to infinity for large time, for $1\le p<3$. In the case of strong solutions we provide sharp estimates both from above and from below and explicit asymptotic profiles. We also show that solutions arising from $(u_0,\theta_0)$ with zero-mean for the initial temperature $\theta_0$ have a special behavior as $|x|$ or $t$ tends to infinity: contrarily to the generic case, their energy dissipates to zero for large time.
 1 : Institut Camille Jordan (ICJ) CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon 2 : Department of Mathematics, University of California Santa Cruz University of California, Santa Cruz
 Domaine : Mathématiques/Equations aux dérivées partielles
 Mots Clés : Boussinesq – energy – heat convection – fluid – dissipation – Navier-Stokes – long time behaviour – blow up at infinity
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 hal-00464890, version 2 http://hal.archives-ouvertes.fr/hal-00464890 oai:hal.archives-ouvertes.fr:hal-00464890 Contributeur : Lorenzo Brandolese <> Soumis le : Mercredi 28 Juillet 2010, 09:30:01 Dernière modification le : Jeudi 17 Mars 2011, 20:07:22