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Pré-Publication, Document De Travail Année : 2010

Large time decay and growth for solutions of a viscous Boussinesq system

Résumé

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.
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Dates et versions

hal-00464890 , version 1 (18-03-2010)
hal-00464890 , version 2 (28-07-2010)

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Lorenzo Brandolese, Maria Elena Schonbek. Large time decay and growth for solutions of a viscous Boussinesq system. 2010. ⟨hal-00464890v1⟩

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