Vanishing viscosity limit of incompressible flow around a small obstacle: A special case

Abstract

In this paper, we consider two dimensional viscous flow around a small obstacle. In [4], the authors proved that the solutions of the Navier-Stokes system around a small obstacle of size ε converge to solutions of the Euler system in the whole space under the condition that the size of the obstacle ε is smaller than a suitable constant K times the kinematic viscosity ν. We show that, if the Euler flow is antisymmetric, then this smallness condition can be removed.

Keywords

• navier-stokes equations
• euler equations
• vanishing viscosity limit
• exterior domain
• boundary layer