On the attractor for 2D Navier-Stokes-like system with the dynamic slip boundary condition in a channel

Abstract

We consider a 2D infinite channel domain with an incompressible fluid satisfying the so-called dynamic slip boundary condition on the (part of the) boundary. Introducing an exhaustion by a sequence of bounded sub-domains of the whole channel we show that the unique weak solution is strong. We then construct the global attractor and find an explicit upper bound of its fractal dimension with regard to the physical parameters. This result is compatible with the analogous estimate in the case of the Dirichlet boundary condition.