Singular limit of 2D second grade fluid past an obstacle

Abstract

In this paper, we consider the 2D second grade fluid past an obstacle satisfying the standard non-slip boundary condition at the surface of the obstacle. Second grade fluid 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 the constraint condition $\nu =o({\alpha }^{\frac{4}{3}})$, the second grade fluid with a suitable initial velocity converges to the Euler fluid as $\alpha$ tends to zero. Moreover, we estimate the convergence rate of the solution of second grade fluid equations to the one of Euler fluid equations as $\nu$ and $\alpha$ approach zero.

References in corpus (4)

• Convergence of the 2D Euler-$\alpha$ to Euler equations in the Dirichlet case: indifference to boundary layers
• Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions
• Global Well-Posedness of 2D Euler-$\alpha$ Equations in Exterior Domain
• Global Well-Posedness of 2D Second Grade Fluid Equations in Exterior Domain