Strong solutions of the Boussinesq system in exterior domains
Abstract We consider the instationary Boussinesq equations in a smooth three-dimensional exterior domain. A strong solution is a weak solution such that the velocity field additionally satisfies Serrin's condition. The crucial point in this concept of a strong solution is the fact that we have required no additional integrability condition for the temperature. We present a sufficient criterion for the existence of such a strong solution. Further we will characterize the class of initial values that allow the existence of such a strong solution in a sufficiently small interval. Finally, we will obtain a uniqueness criterion for weak solutions of the Boussinesq equations which is based on the identification of a weak solution with a strong solution.