Vanishing α and viscosity limits of second grade fluid equations for an expanding domain in the plane. (October 2019)

• Record Type: Journal Article
• Authors: Liu, Jitao; Xu, Wen-Qing
• Is Part Of: Nonlinear analysis. Volume 49(2019)
• Page Start: 355
• Page End: 367
• Publication Date: 2019-10
• Subjects: Vanishing α limits -- Vanishing viscosity limits -- Expanding domain -- Second grade fluid equations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.03.011
• Languages: English
• ISSNs: 1468-1218

Abstract

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.