Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions

This paper concerns the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain. When the initial vorticity is in the Lebesgue space L-q with 2 < q <= infinity, we show that the degenerate viscous lake equations possess a unique global solution and the solution converges to a corresponding weak solution of the inviscid lake equations. In a special case when the vorticity is in L-infinity, an explicit convergence rate is obtained.