Attractors of the velocity–vorticity–Voigt model of the 3D Navier–Stokes equations with damping

Abstract

In this paper, we prove the existence of global and exponential attractors of optimal regularity of a regularization for the three-dimensional Navier–Stokes equations with damping, which is called the three-dimensional velocity–vorticity–Voigt (VVV) system proposed by Larios, Pei and Rebholz (Larios et al., 2019). Differently, there is no “Voigt term”-α2Awt in the second equation of system (1.1) below. The proof is based on some energy estimates in Sobolev spaces and the semigroup decomposition.