The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for ...The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous （inviscid） regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes- Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient v →0.展开更多
This paper is concerned with the existence of pullback attractors for the three dimensional nonautonomous Navier-Stokes-Voight equations for the processes generated by the weak and strong solutions. The main difficult...This paper is concerned with the existence of pullback attractors for the three dimensional nonautonomous Navier-Stokes-Voight equations for the processes generated by the weak and strong solutions. The main difficulty is how to establish the pullback asymptotic compactness via energy equation approach under suitable assumption on external force.展开更多
This paper concerns the long-time behavior for the 2D incompressible Navier-Stokes-Voight equations with distributed delay on a non-smooth domain. Under some assumptions on the initial datum and the delay datum, the e...This paper concerns the long-time behavior for the 2D incompressible Navier-Stokes-Voight equations with distributed delay on a non-smooth domain. Under some assumptions on the initial datum and the delay datum, the existence of compact global attractors is obtained.展开更多
基金supported by the Scientific and Research Council of Turkey (No.106T337)the ISF Grant (No.120/6)+1 种基金the BSF Grant (No.2004271)the National Science Foundation (Nos.DMS-0504619,DMS-0708832)
文摘The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous （inviscid） regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes- Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient v →0.
基金in part supported by the NNSF of China(No.10871040,11671075)supported in part by Ph.D.Innovative Fund of Donghua University(No.104-06-0019089)+2 种基金the Fund of Young Backbone Teacher in Henan Province(No.2018GGJS039)the Key Project of Science and Technology of Henan Province(Grant No.182102410069)supported by the National Natural Science Foundation of China(No.11801357)
文摘This paper is concerned with the existence of pullback attractors for the three dimensional nonautonomous Navier-Stokes-Voight equations for the processes generated by the weak and strong solutions. The main difficulty is how to establish the pullback asymptotic compactness via energy equation approach under suitable assumption on external force.
文摘This paper concerns the long-time behavior for the 2D incompressible Navier-Stokes-Voight equations with distributed delay on a non-smooth domain. Under some assumptions on the initial datum and the delay datum, the existence of compact global attractors is obtained.
