Decay characterization of solutions to incompressible Navier–Stokes–Voigt equations

Recently, Niche [J. Differential Equations, 260 (2016), 4440–4453] established upper bounds on the decay rates of solutions to the 3D incompressible Navier–Stokes–Voigt equations in terms of the decay character r∗ of the initial data in H1(R3). Motivated by this work, we focus on characterizing thelarge-time behavior of all space-time derivatives of the solutions for the 2D case and establish upper bounds and lower bounds on their decay rates by making use of the decay character and Fourier splitting methods. In particular, for the case −n2<r∗⩽1, we verify the optimality of the upper bounds, which is new to the best of our knowledge. Similar improved decay results are also true for the 3D case.