Rigorous derivation of the equations describing objects called “accretion disk” ˇarka Neˇcasov´a S´ ˇ a 25, 115 67 Praha 1, Czech Republic. Institute of Mathematics of the Academy of Sciences, Zitn´

Abstract We study the 3-D compressible barotropic Navier-Stokes-(Fourier)- Poisson system describing the motion of a compressible rotating viscous fluid with renormalized gravitation, confined to a straight layer Ωǫ = ω × (0, ǫ), where ω is a 2-D domain. We shall show that the weak solutions in the 3D domain converge to the strong solution of a rotating 2-D Navier-Stokes-(Fourier)-Poisson system on ω as ǫ → 0 for either all times less than the maximal life time of the strong solution of the 2-D system or the initial data are small √ when the Froude number is small (F r = O( ǫ). We consider just the selfgravity force. In the second case we consider a rotating pure 2-D Navier-Stokes-(Fourier) system on ω as ǫ → 0 when F r = O(1) in the case of the external gravity see [1, 2].

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

References ˇ casov´a, and M. Pokorn´y: The rotating Navier–Stokes– [1] B. Ducomet, M. Caggio, S.Neˇ Fourier–Poisson system on thin domains, Preprint 2016 ˇ casov´a, M. Pokorn´y and M. A. Rodr´ıguez - Bellido: Derivation of the [2] B. Ducomet, S.Neˇ Navier - Stokes - Poisson system for an accretion disk, Preprint 2016

Rigorous derivation of the equations describing objects ...

confined to a straight layer Ωe = ω × (0,ϵ), where ω is a 2-D domain. We shall show that the weak solutions in the 3D domain converge to the strong solution of a ...

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