A generalized existence theorem of pullback attractors and its application to the 3D non-autonomous Navier-Stokes-Voigt equations

In this paper, we first establish a new existence theorem of pullback attractors of the norm-to-weak continuous, weak compact cocycle, and then apply it to the 3D non-autonomous incompressible Navier-Stokes-Voigt equations to directly obtain the existence of pullback attractors in two phase spaces $ X $ and $ Y $ respectively, where there is a compact embedding relationship $ X \hookrightarrow Y $. The new method is first established in the non-autonomous case to verify the existence of the pullback attractors and is different from the existing ones.