Upper bound of decay rate for solutions to the Navier–Stokes–Voigt equations in R3

摘要

In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the Navier–Stokes–Voigt equations in R3. Then we combine the Fourier splitting method of Schonbek and the Gronwall inequality to prove that the solutions have the following decay rates‖∇mu(x,t)‖2+‖∇m+1u(x,t)‖2⩽c(1+t)-3/2-m,for largetwhen u0∈Hm(R3)∩L1(R3) and m=0,1.