Concentration–diffusion phenomena of heat convection in an incompressible fluid

Abstract

We study in the whole space Rⁿ the behaviour of solutions to the Boussinesq equations at large distances. Therefore, we investigate the solvability of these equations in weighted L^∞-spaces and determine the asymptotic profile for sufficiently fast decaying initial data. For n=2,3 we are able to construct initial data such that the velocity exhibits an interesting concentration–diffusion phenomenon.