Chapter 1 Introduction

1.1 The main models

1.2 Notations and some preliminary lemmas

Chapter 2 The Navier-Stokes Equations with Damping

2.1 Introduction

2.2 Existence of weak solutions

2.3 Existence and uniqueness of strong solutions

Chapter 3 Decay of Navier-Stokes Equations with Damping

3.1 Introduction

3.2 A priori estimates on upper bound ofdecay

3.3 A priori estimates on lower bound ofdecay

3.4 The decay ofthe weak solutions

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

4.1 Introduction

4.2 Existence of weak solutions

4.3 Existence and uniqueness of strong solutions

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

5.1 Introduction

5.2 The global existence ofsolutions

5.3 The global stability ofsolutions

Chapter 6 Some Remarks on Planar Boussinesq Equations

6.1 Introduction and the main results

6.2 The case ofsmooth initial data

References