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MiS Preprint
51/2013
Dimension reduction for compressible viscous fluids
Peter Bella, Eduard Feireisl and Antonín Novotný
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 $\Omega_\epsilon = \epsilon Q \times (0,1)$, $Q \subset \mathbb{R}^2$. We show that the weak solutions in the 3D domain converge to (strong) solutions of the limit 1D Navier-Stokes system as $\epsilon \to 0$.
