一些流体模型的整体适定性（英文） 秦玉明 科学出版社 PDF电子教材 PDF电子书 大学教材电子版 电子课本 网盘下载（价值148元）【高清非扫描版】（2023年02月）

《一些流体模型的整体适定性（英文）》秦玉明 科学出版社 PDF电子教材 PDF电子书 大学教材电子版 电子课本 网盘下载（价值148元）【高清非扫描版】（2023年02月）

图书简介：

本书旨在介绍一些关于整体适定性的最新结果，包括一些流体模型整体解的渐近行为，如辐射气体燃烧模型、辐射流体力学模型、Navier-Stokes方程和p次方牛顿流体模型。这些模型具有相似的结构，由Navier-Stokes方程与其他方程或其他效应耦合而成。这本书的大部分材料都基于作者及其合作者近年来进行的研究。有些以前只在原始论文中发表，有些直到现在才发表。

目录：

Foreword　i
CHAPTER　1
Preliminary　1
1.1　Sobolev Spaces and Their Basic Properties　1
1.1.1　Weak Derivatives and Their Properties　1
1.1.2　Sobolev Spaces　4
1.1.3　Some Properties of Sobolev Spaces　5
1.2　Some Inequalities in Analysis　12
1.2.1　The Young Inequality　12
1.2.2　The Poincare Inequality　13
1.2.3　The Bellman-Gronwall Inequality　13
1.2.4　The Holder Inequality　14
1.2.5　The Minkowski Inequality　15
1.2.6　The Jensen Inequality　15
1.2.7　The Shen-Zheng Inequality　16
1.2.8　The Interpolation Inequality　19
1.2.9　The Gagliardo-Nirenberg Interpolation Inequality　19
1.3　Co-Semigroup　20
CHAPTER　2
Global Existence and Exponential Stability of Spherically Symmetric Solutions to a　Compressible Combustion Radiative and Reactive Gas　23
2.1　Introduction　23
2.2　Model and Main Results　24
2.2.1　Combustion Model of Radiative and Reactive Gas　24
2.2.2　Spherical Symmetry Model of Combustion Model　25
2.2.3　Main Theorems　28
2.3　Global Existence and Exponential Stability in H1　30
2.3.1　Global Existence of Solutions in Hl　31
2.3.2　Exponential Stability of Solutions in H1　55
2.4　Global Existence and Exponential Stability in H2　67
2.4.1　Global Existence of Solutions in H2　67
2.4.2　Exponential Stability of Solutions in H2　74
2.5　Global Existence and Exponential Stability in H4　75
2.5.1　Global Existence of Solutions in H4　75
2.5.2　Exponential Stability of Solutions in W4　87
2.6　Bibliographic Comments　90
CHAPTER　3
Global Existence, Uniqueness and Exponential Stability of Solutions for the One-Dimensional Navier-Stokes Equations with Capillarity　93
3.1　Introduction　93
3.2　Model and Main Results　94
3.2.1　Korteweg-Type Model　94
3.2.2　Main Theorems　97
3.3　Global Existence and Exponential Stability in　99
3.3.1　Global Existence in *　99
3.3.2　Asymptotic Behavior in *　114
3.3.3　Exponential Stability in *　120
3.4　Global Existence and Exponential Stability in *　122
3.4.1　Global Existence and Uniqueness in *　122
3.4.2　Exponential Stability in *　125
3.5　Global Existence and Exponential Stability in *　126
3.5.1　Global Existence in *　126
3.5.2　Asymptotic Behavior of Solutions in*　132
3.5.3　Exponential Stability in *　134
3.6　Bibliographic Comments　137
CHAPTER　4
Exponential Stability of Solutions for the Compressible p-th. Power Newtonian Fluid with Large Initial Data　39
4.1　Introduction　39
4.2　Model and Main Results　40
4.3　Global Existence and Exponential Stability in H1　43
4.3.1　Global Existence in H1　43
4.3.2　Exponential Stability in H1　62
4.4　Global Existence and Exponential Stability in H2　63
4.5　Global Existence and Exponential Stability in H4　65
4.6　Bibliographic Comments　66
CHAPTER　5
Global Existence and Asymptotic Behavior of Spherically Symmetric Solutions for the Multi-Dimensional Infrarelativistic Model　169
5.1　Introduction　169
5.2　Reformulation and Main Theorems　171
5.2.1　Reformulation of Model　171
5.2.2　Main Theorems　174
5.3　Global Existence and Asymptotic Behavior in H1　177
5.3.1　Global Existence in Ti}　177
5.3.2　Asymptotic Behavior in H1　196
5.4　Global Existence and Asymptotic Behavior in H2　201
5.4.1　Global Existence in Ti.2　201
5.4.2　Asymptotic Behavior in H2　205
5.5　Global Existence and Asymptotic Behavior in H4　206
5.5.1　Global Existence in H4　206
5.5.2　Asymptotic Behavior in 　219
5.6　Bibliographic Comments　221
CHAPTER　6
Global Existence and Asymptotic Behavior of Cylindrically Symmetric Solutions for the 3D Infrarelativistic Model with Radiation　223
6.1　Introduction　223
6.2　Reformation and Main Results　225
6.2.1　Reformation of Model　225
6.2.2　Main Theorems　228
6.3　Global Existence and Asymptotic Behavior in H1　229
6.3.1　Global Existence in H1　230
6.3.2　Asymptotic Behavior in H1　256
6.4　Global Existence and Asymptotic Behavior in H2　257
6.4.1　Global Existence in H　257
6.4.2　Asymptotic Behavior in H2　260
6.5　Global Existence and Asymptotic Behavior in H4　261
6.5.1　Global Existence in H4　261
6.5.2　Asymptotic Behavior in　273
6.6　Bibliographic Comments　276
Bibliography　277