Hydrostatic approximation and optimal convergence rate for the Second-Grade fluid system

Abstract

This paper is devoted to the study of the Second-Grade fluid system from three aspects. Firstly, we establish the well-posedness of the scaled anisotropic Second-Grade fluid system and the hydrostatic Second-Grade fluid system in a thin strip R×T with convex Gevrey-2 initial data. Secondly, we justify the limit from the anisotropic Second-Grade fluid system to the hydrostatic Second-Grade fluid system. Finally, we prove that the hydrostatic Second-Grade fluid system will converge to the hydrostatic Navier–Stokes system as material parameter goes to zero.