Asymptotic behavior of solutions for a three dimensional system of globally modified Navier–Stokes equations with a locally Lipschitz delay term

Existence, uniqueness, and continuity properties of solutions for a globally modified version of Navier–Stokes equations with finite delay terms within a locally Lipschitz operator are established. Moreover, we also analyze the stationary problem, and, under suitable assumptions, we prove that there exists a unique stationary solution, which is globally asymptotically exponentially stable.