Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media


Type
Article
Change log
Authors
Titi, Edriss S 
Trabelsi, Saber 
Abstract

We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-B'enard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in L2 and H1. Eventually, we comment on the applicability of a data assimilation algorithm to our system.

Description
Keywords
35Q30, 35Q35, 76B03, 86A10, 93C20, 37C50, 76B75, 34D06, math.AP, math.AP
Journal Title
Discrete and Continuous Dynamical Systems: Series S
Conference Name
Journal ISSN
1937-1179
Volume Title
Publisher
American Institute of Mathematical Sciences (AIMS)
Sponsorship
Engineering and Physical Sciences Research Council (EP/R014604/1)