PULLBACK ATTRACTORS FOR STRONG SOLUTIONS OF 2D NON-AUTONOMOUS g-NAVIER-STOKES EQUATIONS

Abstract

Considered here is the first initial boundary value problem for the 2D nonautonomous g-Navier-Stokes equations in bounded domains. We prove the existence of a pullback attractor in V g for the continuous process generated by strong solutions to the problem. We also prove the exponential growth in V g and in H 2 ( , g) for the pullback attractor, when time goes to −∞.

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.…”

“…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]. Recently, the random attractors for the 2D stochastic g-Navier-Stokes equation were researched in [14].…”