一维辐射流体方程组和液晶方程组解的整体存在性、渐近性和正则性（英文）

Thisbookisaimedatpresentingsomerecentresultsonsomenonlinearevolutionaryfluidequations,includingtheglobalwell-posednessandexistenceofattractorsofsolutionstoradiativefluidsequations,liquidcrystalequations.Mostofmaterialsofthisbookarebasedontheresearchcarriedoutbytheauthorsandtheircollaboratorsinrecentyears.Someofithasbeenpreviouslypublishedonlyinoriginalpapers,andsomeofthematerialhasneverbeenpublisheduntilnow.

Contents
Foreword i
CHAPTER 1 Preliminary 1
1.1 Some Basic Inequalities 1
1.1.1 The Sobolev Inequalities 1
1.1.2 The Interpolation Inequalities 5
1.1.3 The Poincare Inequality 6
1.1.4 The Classical Bellman-Gronwall Inequality 7
1.1.5 The Generalized Bellman-Gronwall Inequalities 8
1.1.6 The Uniform Bellman-Gronwall Inequality 9
1.1.7 The Young Inequalities
1.1.8 The Holder Inequalities 13
1.1.9 The Minkowski Inequalities 14
CHAPTER 2 Asymptotic Behavior of Solutions for the One-Dimensional Infrarelativistic Model of a Compressible Viscous Gas with Radiation 17
2.1 Main Results 17
2.2 Global Existence and Uniform-in-Time Estimates in H1 22
2.3 Asymptotic Behavior of Solutions in Hi 48
2.4 Global Existence and Uniform-in-Time Estimates in H2 53
2.5 Asymptotic Behavior of Solutions in H2 60
2.6 Global Existence and Uniform-in-Time Estimates in H4 62
2.7 Asymptotic Behavior of Solutions in H4 81
2.8 Bibliographic Comments 85
CHAPTER 3 Global Existence and Regularity of a One-Dimensional Liquid Crystal System 89
3.1 Main Results 89
3.2 Global Existence in 91
3.3 Proof of Theorem 3.1.2 100
3.4 Proof of Hheorem 3.1.3 103
3.5 Bibliographic Comments 109
CHAPTER 4 Large-time Behavior of Solutions do p One-Dimensional Liquid Crystal System 111
4.1 Introduction 111
4.2 Uniform Estimates in 113
4.3 Laxge-time Behavior in 122
4.4 Bibliographic Comments 134
Bibliography 135
Index 143