Homogenization and singular limits for the complete Navier-Stokes-Fourier system

Eduard Feireisl (1) , Antonin Novotny (2) , Takéo Takahashi (3, 4)

1 Mathematical Institute [Praha] - Academy of Sciences
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 IECN - Institut Élie Cartan de Nancy
4 CORIDA - Robust control of infinite dimensional systems and applications

In this paper we apply the methods of homogenization to the full Navier-Stokes-Fourier system describing the motion of a general viscous, compressible, and heat conducting fluid. We study the asymptotic behavior of solutions in perforated domains with tiny holes, where the diameter of the holes is proportional to their mutual distance. As a limit system, we identify a porous medium type equation with a nonlinear Darcy's law.

Mots clés: Compressible Navier-Stokes-Fourier equations; Homogenization; Porous medium equation

Domaines: Equations aux dérivées partielles [math.AP]

Eduard Feireisl, Antonin Novotny, Takéo Takahashi. Homogenization and singular limits for the complete Navier-Stokes-Fourier system. Journal de Mathématiques Pures et Appliquées, 2010, 94 (1), pp.33-57. ⟨10.1016/j.matpur.2009.11.006⟩. ⟨hal-00590620⟩