醉染图书非牛顿流:动力系统方法(英文版)9787030595584

Introduction
1 Non-Newtonlan fluids and their mathematical model
1.1 Non-Newtonian fluids and their characteristics
1.2 Incompressible and isothermal bipolar non-Newtonian fluids models
1.3 isothermal compressible viscous fluids models
1.4 Other related models
2 Global solutions to the equations of non-Newtonlan fluids
2.1 Global solutions to the periodic initial value problems for the incompressible non-Newtonian fluids
2.1.1 Existence and uniqueness of global solutions to the incompressible bipolar fluids
2.1.2 Existence of weak solutions to the incompressible monopo[ar fluids
2.2 Global solutions to the compressible non-Newtonian fluids - Existence and uniqueness of weak solution to the bipolar compressible non-Newtonian fluids
. Time-periodic solutions to the incompressible bipolar fluids
..1 Time-periodic weak solutions to the incompressible bipolar fluids
..2 Existence and uniqueness of strong time-periodic solutions to the incompressible bipolar fluids
2.4 Existence and uniqueness and stability of global solutions to the initial boundary value problems for the incompressible bipolar viscous fluids
2.4.1 Existence
2.4.2 Regularity
2.4.3 Uniqueness
2.4.4 Stability
2.5 The periodic initial value problem and initial value problem for the modified Boussinesq approximation
2.6 Periodic initial value problem and initial value problem for the non-Newtonian-Boussinesq approximation
3 Global attractors of incompressible non-Newtonian fluids
3.1 Global attractors of incompressible non-Newtonian fluids on bounded domain
3.1.1 Existence of Absorbing Sets
3.1.2 Consistently differentiability for the solution semigroup
3.1.3 For μ1 > O, the upper bounded estimates of dH(Aμ1) and dF(Aμ1) of attractor Aμ1
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(Ω) 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.. 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 Numerica xermets
8.3.6 Two-dimensional problem
8.3.7 Conclusion
Bib|iography
Index