Hm Convergence of the Second-Grade Fluid Equations to Euler Equations in ℝd

In this paper, we investigate an approximation of the Euler equation by the second-grade fluid equations in ℝdd=2,3. The convergence in Hm of a sequence of solutions to the second-grade fluid equations in a uniform interval is proven as both the viscosity coefficient ν and filter parameter α tend to zero with an initial velocity in Hm.