黏性不可压流体建模

《黏性不可压流体建模》讨论了不可压流体压其相关模型，特别是齐次、非齐次和带有阻尼项的不可压NaVleeStokes方程组与二维Boussinesq方程组。这些方程是流体力学中的基本方程，在非线性偏微分方程、动力系统、科学计算等领域中占有十分重要的位置。主要阐述了非齐次不可压NavierStokes方程stokes逼近系统解的存在性，带有阻尼项的不可压NavlerStokes方程解的适定性。非齐次不可压的NavierStokes方程大解的整体稳定性，二维Bousslnesq方程古典解的整体存在性等内容。

黏性不可压流体建模内容简介

《黏性不可压流体建模》适合偏微分方程专业的研究生、教师和有关的科学工作者参考。书末附有较详细的参考文献，便于读者在这一方向上开展研究工作。

黏性不可压流体建模图书目录

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

Referenees

黏性不可压流体建模文摘

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The uniqueness of weak solutions is completely open in alldimensions even in two dimensions.Of course,the uniqueness ofsolutions is close to the regularity of solutions.It has been wellknown that the solution which is regular enough is unique and anyweak solution is equal to a strong one if the later exists [38[.However,we can't expect full regularity results to be known since they would imply regularityresults for the homogeneous Navier-Stokes equations (1.6).

The existence of strong solutions was obtained by Kazhikov andhis collaborators.They assumed that μ is a constant and po isbounded away from 0 and proved the local existence of unique strongsolution for all sufficiently regular data.This result was later extendedby Ladyzhenskaya and Solonnikov,Padula,Salvi.But theyall required that the initial density may not vanish (i.e.non-vacuum).Later,Choe and Kim obtained an local existence result on strongsolutions with nonnegative densities in case that μ is a constant.Recently,they proved the local existence of unique strongsolutions in a bounded domain Ω of Rn(n = 2,3) for all initial datasatisfying a natural compatibility condition in the case when μdepends on p and the initial density p0 may vanish in an open subsetofΩ.

黏性不可压流体建模编辑推荐

《黏性不可压流体建模》适合偏微分方程专业的研究生、教师和有关的科学工作者参考。书末附有较详细的参考文献，便于读者在这一方向上开展研究工作。

黏性不可压流体建模目录

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

Referenees