The rotating Navier–Stokes–Fourier–Poisson system on thin domains

Article type: Research Article

Authors: Ducomet, Bernard^a | Caggio, Matteo^b | Nečasová, Šárka^{b; *} | Pokorný, Milan^c

Affiliations: [a] Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, 61 avenue du Général de Gaulle, 94010 Créteil Cedex 10, France. E-mail: [email protected] | [b] Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic. E-mails: [email protected], [email protected] | [c] Charles University, Faculty of Mathematics and Physics, Math. Institute of Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider the compressible Navier–Stokes–Fourier–Poisson system describing the motion of a viscous heat conducting rotating fluid confined to a straight layer Ωϵ=ω×(0,ϵ), where ω is a 2-D domain. The aim of this paper is to show that the weak solutions in the 3-D domain converge to the strong solution of the 2-D Navier–Stokes–Fourier–Poisson system on ω as ϵ→0 on the time interval, where the strong solution exists. We consider two different regimes in dependence on the asymptotic behaviour of the Froude number.

Keywords: Navier–Stokes–Fourier–Poisson system, weak solution, entropy, rotation, accretion disk, thin domains, dimension reduction, strong solution

DOI: 10.3233/ASY-181472

Journal: Asymptotic Analysis, vol. 109, no. 3-4, pp. 111-141, 2018