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O, the upper bounded estimates of dH(A¦Ì1) and dF(A¦Ì1) of attractor A¦Ì1 3.2 Global attractors of incompressible non-Newtonian fluids on unbounded domain 3.3 Exponential attractors of incompressible non-Newtonian fluids 3.3.1 Estimates for the nonlinear terms 3.3.2 Compressibility on L2(¦¸) Global attractors of modified Boussinesq approximation 5 Inertial manifolds of incompressible non-Newtonian fluids 5.1 Inertial manifolds of incompressible bipolar non-Newtonian fluids 5.1.1 Lipschitz property 5.1.2 The squeezing property 5.1.3 Fixed-point theorem 5.1.4 Inertial manifolds 5.2 Approximated inertial manifolds of incompressible bipolar non-Newtonian fluids 5.2.1 The analyticity in time and behavior of higher order modes 5.2.2 Approximated inertial manifolds 6 The regularity of solutions and related problems 6.1 Stationary solutions of the incompressible bipolar non-Newtonian fluids 6.2 Decay estimates of one kind of incompressible monopolar non-Newtonian fluid 6.3 Partial regularity of one kind of incompressible monopolar non-Newtonian fluid 6.4 The convergence of solution and attractors between one kind of incompressible non-Newtonian fluid and the Newtonian fluids 6.5 Other decay estimates of incompressible non-Newtonian fluids 7 Global attractors and time-spatial chaos 7.1 Global attractor of low regularity 7.2 Attractors and their spatial complexity of reaction-diffusion equations on bounded domain 8 Non-Newtonian generalized fluid and their applications 8.1 An inverse problem of a heated generalized second grade fluid 8.1.1 Formulation 8.1.2 Outline of the optimization method 8.1.3 Illustrative examples 8.2 A numerical study of a generalized Maxwell fluid through a porous medium 8.2.1 Mathematical model 8.2.2 HPM solutions 8.2.3 Numerical results and discussion 8.2.4 Conclusions 8.3 Viscoelastic fluid with fractional derivative models 8.3.1 Preliminaries 8.3.2 Eigenfunction expansion of the solution and properties of the time-dependent components 8.3.3 Finite difference approximation 8.3.4 Duhamel-type representation of the solution 8.3.5 Numerical experiments 8.3.6 Two-dimensional problem 8.3.7 Conclusion Bib|iography Index