一維輻射流體方程組和液晶方程組解的整體存在性漸近性和正則性(英文版)
內容大鋼
This book presents recent results on nonlinear evolutionarv fluid equations, in particular the global well-posedness and asvmptotic behavior of solutions to 1D radiative fluid equations, as well as liquid crvstal equations. Most of the material in this book was prepared bv the author over the past few vears.
This book has two main features. Firstlv, there are more known results on higher dimensional radiative fluid svstems but only on the local existence and explosion of solutions; while the existing findings on the one-dimensional case present some shortcomings, this book introduces corrections and improvements of these shortcomings. SecondlV, the current findings on the high-dimensional compressible liquid crvstal fluid equations are few and include onlv globallv existing solutions but not the asvmptotic behavior of the solutions; the author developed not onlv the global existence and regularitv of the solutions, but also the asvmptotic behavior of the solutions for the one-dimensional case in the chapter 3 of this book. Therefore, this work provides the reader with complete elements related to the one-dimensional compressible liquid crvstal fluid svstem.
作者介紹
編者:秦玉明
秦玉明 is full professor, head of Mathematics Department and director of Institute of Nonlinear Sciences of Donghua Universitv. His research interests are global (local) wellposedness of solutions and infinite dimensional dvnamical svstems for nonlinear evolutionarv equations including fluid equations such as Navier-Stokes equations, MHD, and thermos-viscoelastic equations.
目錄
Foreword
CHAPTER 1 Preliminary
1.1 Some Basic Inequalities
1.1.1 The Sobolev Inequalities
1.1.2 The Interpolation Inequalities
1.1.3 The Poincar6 Inequality
1.1.4 The Classical Bellman-Gronwall Inequality
1.1.5 The Generalized Bellman-Gronwall Inequalities
1.1.6 The Uniform Bellman-Gronwall Inequality
1.1.7 The Young Inequalities
1.1.8 The H61der Inequalities
1.1.9 The Minkowski Inequalities
CHAPTER 2 Asymptotic Behavior of Solutions for the One-Dimensional Infrarelativistic Model of a Compressible Viscous Gas with Radiation
2.1 Main Results
2.2 Global Existence and Uniform-in-Time Estimates in H1
2.3 Asymptotic Behavior of Solutions in H1
2.4 Global Existence and Uniform-in-Time Estimates in H2
2.5 Asymptotic Behavior of Solutions in H2
2.6 Global Existence and Uniform-in-Time Estimates in H4
2.7 Asymptotic Behavior of Solutions in H4
2.8 Bibliographic Comments
CHAPTER 3 Global Existence and Regularity of a One-Dimensional Liquid Crystal System
3.1 Main Results
3.2 Global Existence in H1 × H01 × H2
3.5 Bibliographic Comments
CHAPTER 4 Large-time Behavior of Solutions to a One-Dimensional Liquid Crystal System
4.1 Introduction
4.2 Uniform Estimates in Hi x H0i Hi+1 (i = 1, 2) and H4 × H04 × H4
4.3 Large-time Behavior in Hi x H0i x Hi+1 (i = 1, 2) and H4 × H04 H4
4.4 Bibliographic Comments
Bibliography
Index
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