Long-time behaviour of fluid motions in porous media according to the Brinkman model

Rionero, S. and Vergori, L. (2010) Long-time behaviour of fluid motions in porous media according to the Brinkman model. Acta Mechanica, 210(3-4), pp. 221-240. (doi: 10.1007/s00707-009-0205-0)

Abstract

The paper is concerned with a binary fluid mixture in a porous horizontal layer according to the Brinkman model. The long-time behaviour of the solutions is considered: absorbing sets are shown to exist, and the stability (instability) of the rest state is studied. Following the new approach introduced in Rionero (J. Math. Anal. Appl. 333, 1036–1057 (2007)), the global stability of the rest state is rigorously reduced to the stability of the zero solution of a linear binary system of ODEs. The results obtained are extended to cover the presence of a uniform rotation about a vertical axis.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vergori, Dr Luigi
• Authors: Rionero, S., and Vergori, L.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Acta Mechanica
• Publisher: Springer Verlag
• ISSN: 0001-5970
• ISSN (Online): 1619-6937