Well-posedness and asymptotic behaviour for the Bousinessq system in Rn

Abstract

We analyze the well-posedness of the initial value problem for a Convection Problem. Mild solutions are obtained in the weak-L p (R n) spaces and the existence of self-similar solutions is showed, while the only small self-similar solution in the Lebesgue space L p (R n) is the null solution. The asymptotic stability of solutions is analyzed and, as a consequence, a criterium of self-similarity persistence at large times is obtained.