Modelling degradating dispersions in a three dimensional finite container under general boundary conditions

This paper deals with a mathematical model widely used to analyze the evolution of a dispersion of bubbles in a liquid. The model takes into account both diffusion and buoyancy in a finite three-dimensional container. Rather general Dirichlet as well as Neumann boundary conditions are allowed. We prove the well-posedness of the initial-boundary value problem. The unique solution is classical and global in time