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
A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system i...A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.展开更多
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Supported by the NNSF of China(19972058) and the NSF of Yunnan Province (2001A0001M).
文摘A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.
