Ghost effect by curvature in planar Couette flow

Leif Arkeryd (1) , Raffaele Esposito (2) , Rossana Marra , Anne Nouri (3)

1 Chalmers University of Technology [Göteborg]
2 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
3 I2M - Institut de Mathématiques de Marseille

We study a rarefied gas, described by the Boltzmann equation, between two coaxial rotating cylinders in the small Knudsen number regime. When the radius of the inner cylinder is suitably sent to infinity, the limiting evolution is expected to converge to a modified Couette flow which keeps memory of the vanishing curvature of the cylinders (ghost effect). In the 1-d stationary case we prove the existence of a positive isolated L_2-solution to the Boltzmann equation and its convergence. This is obtained by means of a truncated bulk-boundary layer expansion which requires the study of a new Milne problem, and an estimate of the remainder based on a generalized spectral inequality.

Domaines: Physique mathématique [math-ph]

Leif Arkeryd, Raffaele Esposito, Rossana Marra, Anne Nouri. Ghost effect by curvature in planar Couette flow. Kinetic and Related Models , 2011, 4 (1), pp.109-138. ⟨10.3934/krm.2011.4.109⟩. ⟨hal-01177113⟩