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

In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a well-known non-Newtonian fluid model, with two parameters alpha which represents the length-scale, while nu > 0 corresponds to the viscosity. We prove that, as nu, alpha tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that nu= o(alpha (4)/(3)). Moreover, the convergent rate is obtained. .

Automated summary

In this paper, the authors study the second-grade fluid equations in a 2D exterior domain with non-slip boundary conditions. The second-grade fluid model is a well-known non-Newtonian fluid model, with alpha representing the length scale and nu > 0 representing the viscosity. The authors prove that as nu and alpha tend to zero, the solution of the second-grade fluid equations converges to the solution of the Euler equations with suitable initial data, provided that nu = o(alpha(4)/(3)). The convergent rate is also obtained.