Decay rate of solutions to 3D Navier-Stokes-Voigt equations in Hm spaces

In this paper, we first prove the regularity in H-m(R-3) of weak solutions to the Navier-Stokes-Voigt equations with initial data in H-K (R-3) for all m <= K. Then we compute the upper bound of decay rate for these solutions, specifically, we prove that parallel to del(m)(u)(t)parallel to(2) + parallel to del(m+1)(u)(t)parallel to(2) <= c(1+t)(-3/2-m), for large t, when u(0) is an element of H-sigma(m+1)(R-3) boolean AND L-1(R-3), m is an element of N. (C) 2016 Elsevier Ltd. All rights reserved.