A Subdiffusive Navier–Stokes–Voigt System

For nu is an element of (0, 1), we analyze the system of equations on the two dimensional domain Omega in the unknown function u = (u(1)(x, t), u(2)(x, t)) {u(t) - mu Delta u - gamma Delta partial derivative(nu)(t)u + u . del u = -Delta p + f, div u = 0, where partial derivative(nu)(t) denotes the Riemann-Liouville fractional derivative of order nu. Under suitable conditions on the given data, the global existence and uniqueness of strong solutions to the related initial-boundary value problems are established for nu is an element of (0, 1/2). The convergence of the strong solution to the one of the corresponding initial-boundary value problem to the Navier-Stokes equations is discussed, in the limit nu -> 0. We also present several numerical tests illustrating this convergence. (C) 2020 Elsevier B.V. All rights reserved.