Pullback attractor of 2D nonautonomous g-Navier-Stokes equations with linear dampness

Abstract

The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness are investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.

The Long-Time Behavior of 2D Nonautonomous g -Navier-Stokes Equations with Weak Dampness and Time Delay

“…The understanding of the behavior with dynamical systems was one of the most important problems of modern mathematical physics (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). In the last decades, g-Navier-Stokes equations have received increasing attention due to their importance in the fluid motion.…”

“…The Hausdorff and fractal dimension of the global attractor about the 2D g-Navier-Stokes equation for the periodic and Dirichlet boundary conditions and the global attractor of the 2D g-Navier-Stokes equation on some unbounded domains were researched in [5]. In [6][7][8][9][10], the finite dimensional global attractor and the pullback attractor for g-Navier-Stokes equation were studied. Moreover, Anh et al studied long-time behavior for 2D nonautonomous g-Navier-Stokes equations and the stability of solutions to stochastic 2D g-Navier-Stokes equation with finite delays in [11,12]; Quyee researched the stationary solutions to 2D g-Navier-Stokes equation and pullback attractor for 2D g-Navier-Stokes equation with infinite delays in [13].…”

Weak solutions to the time-fractional g-Bénard equations

“…The derived equations are called the g-Navier-Stokes equations. This theory has interested many researchers in recent years, see [4,5,13] and the references therein.…”