Abstract
We consider the long time behavior of weak and strong solutions of the $n$-dimensional viscous Boussinesq system in the half space, with $n\geq3$. The $L^r(\mathbb{R}^n_+)$-asymptotics of strong solutions and their first three derivatives, with $1\leq r\leq\infty$, are derived by combining $L^q-L^r$ estimates and properties of the fractional powers of the Stokes operator. For the $L^\infty-$asymptotics of the second order derivatives, the unboundedness of the projection operator $P: L^\infty(\mathbb{R}^n_+)\rightarrow L^\infty_\sigma(\mathbb{R}^n_+)$ is dealt with by an appropriate decomposition of the nonlinear term.
Citation
Pigong Han. Maria E. Schonbek. "Large time decay properties of solutions to a viscous Boussinesq system in a half space." Adv. Differential Equations 19 (1/2) 87 - 132, January/February 2014. https://doi.org/10.57262/ade/1384278133
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