Vanishing α and viscosity limits of second grade fluid equations for an expanding domain in the plane. (October 2019) - Liu, Jitao; Xu, Wen-Qing
Abstract: In this paper, we study the asymptotic behavior of solutions to second grade fluid equations, a model for viscoelastic fluids, in an expanding domain. We prove that, the solutions converge to a solution of the incompressible Euler equations in the whole plane, as the elastic response α and the viscosity ν vanish, and the radius of domain becomes infinite. Meanwhile, we also establish precise convergence rates in terms of ν, α and the radius of the family of spatial domains.