Dimension reduction for compressible viscous fluids

Peter Bella, Eduard Feireisl, and Antonín Novotný

Contact the author: Please use for correspondence this email.
Submission date: 17. May. 2013
Pages: 15
published in: Acta applicandae mathematicae, 134 (2014) 1, p. 111-121 
DOI number (of the published article): 10.1007/s10440-014-9872-5
Bibtex
Keywords and phrases: Compressible Navier-Stokes system, dimension reduction, thin rod
Download full preprint: PDF (282 kB)

Abstract:
We consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a cavity shaped as a thin rod Ω_ϵ = ϵQ× (0,1), Q ⊂ ℝ². We show that the weak solutions in the 3D domain converge to (strong) solutions of the limit 1D Navier-Stokes system as ϵ → 0.