Concentration–diffusion phenomena of heat convection in an incompressible fluid

Article type: Research Article

Authors: Farwig, Reinhard^; | Schulz, Raphael | Yamazaki, Masao

Affiliations: Department of Mathematics, Darmstadt University of Technology, 64283 Darmstadt, Germany. E-mail: farwig@mathematik.tu-darmstadt.de | Mathematics Department, University of Erlangen-Nuremberg, 91058 Erlangen, Germany. E-mail: raphael.schulz@math.fau.de | Department of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo, Japan. E-mail: masao.yamazaki@waseda.jp

Note: [] Corresponding author. E-mail: farwig@mathematik.tu-darmstadt.de

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.

Keywords: instationary Boussinesq equations, rate of decay in space, mild and strong solutions, weighted spaces, concentration–diffusion

DOI: 10.3233/ASY-131211

Journal: Asymptotic Analysis, vol. 88, no. 1-2, pp. 17-41, 2014