In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the ...In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given.展开更多
In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forc...In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.展开更多
In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() ...In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() and prove that the Davey-Stewartson system possesses a compact global attractor Ap in Lp(). Furthermore, one show that the attractor is in fact independent of p and prove the attractor has finite Hausdorff and fractal dimensions.展开更多
基金Project supported by the National Natural Science Fundation of China (No. 11171269)the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2012JM1012)the Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 12JK0849)
文摘In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given.
文摘In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.
基金This project is supported Supported by National Natural Science Foundation of China.
文摘In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() and prove that the Davey-Stewartson system possesses a compact global attractor Ap in Lp(). Furthermore, one show that the attractor is in fact independent of p and prove the attractor has finite Hausdorff and fractal dimensions.
