Attractors Of The Velocity-vorticity-Voigt Model Of The 3D Navier-Stokes Equations With Damping

In this paper,we are concerned with the asymptotic dynamical behaviors of the solutions for the velocity-vorticity-Voigt model of the autonomous three-dimensional Navier-Stokes equations with damping subjected to Dirichlet boundary conditions,the asymptotic behaviors of the solutions can be characterized by the global and exponential attractors.The three-dimensional velocity-vorticity-Voigt system is proposed by Larios,Pei and Rebholz,which is coupled the velocity equation with the vorticity equation.The three authors exploited the Galerkin approximation and energy estimate to prove the global well-posedness of the solutions.We study the global well-posedness of the solutions and the existence of the attractors for the three-dimensional velocity-vorticity-Voigt model with damping in this article.When the damping coefficient is greater than some constant,we take advantage of the coupling relationship between velocity equation and vorticity equation to obtain the existence of an absorbing set by energy estimates.Finally,we can prove the existence of the global and exponential attractors by using the method of semigroup decomposition.