《黏性不可壓流體建模》討論了不可壓流體壓其相關模型，特別是齊次、非齊次和帶有阻尼項的不可壓NaVleeStokes方程組與二維Boussinesq方程組。這些方程是流體力學中的基本方程，在非線性偏微分方程、動力系統、科學計算等領域中占有十分重要的位置。主要闡述了非齊次不可壓NavierStokes方程stokes逼近系統解的存在性，帶有阻尼項的不可壓NavlerStokes方程解的適定性。非齊次不可壓的NavierStokes方程大解的整體穩定性，二維Bousslnesq方程古典解的整體存在性等內容。
基本介紹
- 書名：黏性不可壓流體建模
- 作者：蔡曉靜
- 出版日期：2012年11月1日
- 語種：英語
- ISBN：9787118082616
- 品牌：國防工業出版社
- 外文名：Some Studies on the Incompressible Fluids and Related Problems
- 出版社：國防工業出版社
- 頁數：108頁
- 開本：32
- 定價：36.00
內容簡介,圖書目錄,文摘,編輯推薦,目錄,
內容簡介
《黏性不可壓流體建模》適合偏微分方程專業的研究生、教師和有關的科學工作者參考。書末附有較詳細的參考文獻，便於讀者在這一方向上開展研究工作。
圖書目錄
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
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
文摘
著作權頁：
插圖：
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.
插圖：
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.
編輯推薦
《黏性不可壓流體建模》適合偏微分方程專業的研究生、教師和有關的科學工作者參考。書末附有較詳細的參考文獻，便於讀者在這一方向上開展研究工作。
目錄
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
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
