Attractors for the inhomogeneous incompressible Navier–Stokes flows. (February 2023) - Han, Pigong; Lei, Keke; Liu, Chenggang; Wang, Xuewen
Abstract: This paper is devoted to the evolution of Lions's weak solutions to the inhomogeneous Navier–Stokes equations. After proving that the kinetic energy is eventually bounded, we obtain a weakly compact global attractor that all Lions's weak solutions approach as time tends to infinity. Furthermore, the existence of attracting sets in strong topology is established for short trajectories satisfying an additional compactness condition on the density.