黏性不可压流体建模 英文PDF电子书下载

Chapter 1 Introduction 1

1.1 The main models 1

1.2 Notations and some preliminary lemmas 10

Chapter 2 The Navier-Stokes Equations with Damping 13

2.1 Introduction 13

2.2 Existence of weak solutions 15

2.3 Existence and uniqueness of strong solutions 21

Chapter 3 Decay of Navier-Stokes Equations with Damping 29

3.1 Introduction 29

3.2 A priori estimates on upper bound ofdecay 32

3.3 A priori estimates on lower bound ofdecay 38

3.4 The decay ofthe weak solutions 42

Chapter 4 Stokes Approximation of Non-homogeneous Navier-Stokes Equations 48

4.1 Introduction 48

4.2 Existence of weak solutions 51

4.3 Existence and uniqueness of strong solutions 60

Chapter 5 Large Solutions to Non-homogeneous Navier-Stokes Equations 67

5.1 Introduction 67

5.2 The global existence ofsolutions 69

5.3 The global stability ofsolutions 74

Chapter 6 Some Remarks on Planar Boussinesq Equations 89

6.1 Introduction and the main results 89

6.2 The case ofsmooth initial data 91

References 103