We consider the equations governing the motion of incompressible second grade fluids in a bounded two-dimensional domain with Navier-slip boundary conditions. We first prove that the corresponding solutions are uniformly bounded with respect to the normal stress modulus α in the L∞-H1 and the L2-H2 time-space norms. Next, we study their asymptotic behavior when α tends to zero, prove that they converge to regular solutions of the Navier-Stokes equations and give the rate of convergence in terms of α.
- Navier-slip boundary conditions
- Navier-Stokes equations
- Rate of convergence
- Second grade fluids
- Uniform a priori estimates