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 of decay
3.3 A priori estimates on lower bound of decay
3.4 The decay of the 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 of solutions
5.3 The global stability of solutions
Chapter 6 Some Remarks on Planar Boussinesq Equations.
6.1 Introduction and the main results
6.2 The case of smooth initial data
References
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