Uniqueness Criteria and Strong Solutions of the Boussinesq Equations in Completely General Domains

Abstract

Consider the instationary Boussinesq equations in a completely general domain $\Omega \subseteq {\mathbb{R}}^3$ and a time interval $[0,T[$. We deal with existence of strong solutions of the Boussinesq equations. These results will be used to prove uniqueness criteria for the Boussinesq equations which are based on the local or global identification of a weak solution with a strong solution.