Global well-posedness of three-dimensional incompressible Boussinesq
system with temperature-dependent viscosity
Abstract
In this paper, we focus on the global well-posedness of solutions to
three-dimensional incompressible Boussinesq equations with
temperature-dependent viscosity under the smallness assumption of
initial velocity fields $u_0$ in the critical space
$\dot_{B}_{3,1}^0$. The key ingredients here
lie in the decomposition of the velocity fields and the regularity
theory of the Stokes system, which are crucial to get rid of the
smallness restricition of the initial temperature $ heta_0$. In
addition, we mention that the improved decay estimates in time is also
necessary.