The Singular Limit of Second-Grade Fluid Equations in a 2D Exterior Domain

In this paper, we consider the 2D second grade fluid past an obstacle satisfying standard non-slip boundary condition at surface of obstacle. Second model is a well-known non-Newtonian model, with two parameters: $\alpha$ representing length-scale, while $\nu > 0$ corresponding to viscosity. We prove that, under constraint = {o}(\alpha^\frac{4}{3})$, suitable initial velocity converges Euler as tends zero. Moreover, estimate convergence rate solution equations one $\nu$ and approach