Concentration–diffusion phenomena of heat convection in an incompressible fluid
Reinhard Farwig, Raphael Schulz, Masao Yamazaki · Asymptotic Analysis · 2014
We study in the whole space R n 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.