  We consider the d-dimensional Boussinesq system defined on a sufficiently
smooth bounded domain, with homogeneous boundary conditions, and subject to
external sources, assumed to cause instability. The initial conditions for both
fluid and heat equations are taken of low regularity. We then seek to uniformly
stabilize such Boussinesq system in the vicinity of an unstable equilibrium
pair, in the critical setting of correspondingly low regularity spaces, by
means of explicitly constructed, feedback controls, which are localized on an
arbitrarily small interior subdomain. In addition, they will be minimal in
number, and of reduced dimension: more precisely, they will be of dimension
$(d-1)$ for the fluid component and of dimension $1$ for the heat component.
The resulting space of well-posedness and stabilization is a suitable, tight
Besov space for the fluid velocity component (close to $\mathbf{L}^3(\Omega$)
for $ d = 3 $) and the space $L^q(\Omega$) for the thermal component, $ q > d
$. Thus, this paper may be viewed as an extension of \cite{LPT.1}, where the
same interior localized uniform stabilization outcome was achieved by use of
finite dimensional feedback controls for the Navier-Stokes equations, in the
same Besov setting.
