The Cauchy problem and decay rates for strong solutions of a Boussinesq system (Q2495038)

Summary: The Boussinesq equations \[ \frac {\partial{\mathbf u}}{\partial t}-\nu\Delta{\mathbf u}+{\mathbf u}\cdot\nabla{\mathbf u}+\nabla\pi=\theta{\mathbf f}, \qquad \operatorname{div}{\mathbf u}=0\quad\text{in }(0,T)\times\mathbb R^3, \] \[ \frac {\partial\theta}{\partial t}-\chi\Delta\theta+{\mathbf u}\cdot\nabla\theta=0\quad\text{in }(0,T)\times\mathbb R^3, \] \[ {\mathbf u}(0,x)={\mathbf a}(x),\;\theta(0,x)=b(x)\quad\text{in }\mathbb R^3, \] describe the motion of an incompressible viscous fluid subject to convective heat transfer. Decay rates of derivatives of solutions of the three-dimensional Cauchy problem for a Boussinesq system are studied.