Large time decay properties of solutions to a viscous Boussinesq system in a half space

Abstract

We consider the long time behavior of weak and strong solutions of the n-dimensional viscous Boussinesq system in the half space, with $n\ge 3$ . The $L^r(R_{+}^n)$-asymptotics of strong solutions and their first three derivatives, with $1\le r\le \infty$, are derived 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 $P:L^{\infty }(R_{+}^n)\to L_{\sigma }^{\infty }(R_{+}^n)$ is dealt by an appropriate decomposition of the nonlinear term.

References in corpus (1)

• Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces

Cited by in corpus (1)

• Remarks on asymptotic behaviors of strong solutions to a viscous Boussinesq system