Existence and decay of solutions in full space to Navier–Stokes equations with delays

Abstract

We consider the Navier–Stokes equations with delays in R n , 2 ≤ n ≤ 4 . We prove existence of weak solutions when the external forces contain some hereditary characteristics and uniqueness when n = 2 . Moreover, if the external forces satisfy a time decay condition we show that the solution decays at an algebraic rate.