In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Mira...In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7, 8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.展开更多
This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajector...This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.展开更多
Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-depende...Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation.Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids.Using the trajectory approach,the authors prove the existence of the trajectory attractor for both systems.展开更多
In this paper,firstly,the proper function space is chosen,and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstra...In this paper,firstly,the proper function space is chosen,and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation,by which the definition of the weak solution of the atmospheric equations is made.Secondly,the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method.The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations.The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors.Moreover,the methods used here are also valid for studying the other atmospheric motion models.展开更多
基金supported by NSFC Grant (11031003)the Fundamental Research Funds for the Central Universities+1 种基金support by Fund of excellent young teachers in Shanghai (shgcjs008)Initial Fund of SUES (A-0501-11-016)
文摘In this article, we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory. For this purpose, we will apply the method presented by Chepyzhov and Miranville [7, 8], in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.
基金Supported by NSFC(51209242,2011BAB09B01,11271290)NSF of Zhejiang Province(LY17A010011)
文摘This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.
基金supported by the Italian MIUR-PRIN Research Project 2008 "Transizioni di fase,isteresi e scale multiple"
文摘Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation.Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids.Using the trajectory approach,the authors prove the existence of the trajectory attractor for both systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.10371011 and 90511009).
文摘In this paper,firstly,the proper function space is chosen,and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation,by which the definition of the weak solution of the atmospheric equations is made.Secondly,the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method.The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations.The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors.Moreover,the methods used here are also valid for studying the other atmospheric motion models.
