Global Well-Posedness for Some Fluid Models
Published on 12. July 2023
292 pages
978-2-7598-2906-4 (ISBN)
Description
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Edition
Digital original
Language
English
Place of publication
Les Ulis
France
Target group
Professional and scholarly
US School Grade: College Graduate Student
Edition type
Digital original
ISBN-13
978-2-7598-2906-4 (9782759829064)
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Schweitzer Classification
Persons
Qin Yuming :
Dr. Yuming QIN is full professor, head of Mathematics Department and director of Institute of Nonlinear Sciences of Donghua University. His research interests are global (local) wellposedness of solutions and infinite-dimensional dynamical systems for nonlinear evolutionary equations including fluid equations such as Navier-Stokes equations, MHD, etc, and thermo(visco)elasticequations.ZHANG Jianlin :
Dr. Jianlin ZHANG is associate Professor in College of Science, Zhongyuan University of Technology since 2012.
Dr. Yuming QIN is full professor, head of Mathematics Department and director of Institute of Nonlinear Sciences of Donghua University. His research interests are global (local) wellposedness of solutions and infinite-dimensional dynamical systems for nonlinear evolutionary equations including fluid equations such as Navier-Stokes equations, MHD, etc, and thermo(visco)elasticequations.ZHANG Jianlin :
Dr. Jianlin ZHANG is associate Professor in College of Science, Zhongyuan University of Technology since 2012.
Content
- Intro
- Global Well-Posedness for Some Fluid Models
- Contents
- Foreword
- Preliminary
- Sobolev Spaces and Their Basic Properties
- Weak Derivatives and Their Properties
- Sobolev Spaces
- Some Properties of Sobolev Spaces
- Some Inequalities in Analysis
- The Young Inequality
- The Poincaré Inequality
- The Bellman-Gronwall Inequality
- The Hölder Inequality
- The Minkowski Inequality
- The Jensen Inequality
- The Shen-Zheng Inequality
- The Interpolation Inequality
- The Gagliardo-Nirenberg Interpolation Inequality
- C0-Semigroup
- Global Existence and Exponential Stability of Spherically Symmetric Solutions to a Compressible Combustion Radiative and Reactive Gas
- Introduction
- Model and Main Results
- Combustion Model of Radiative and Reactive Gas
- Spherical Symmetry Model of Combustion Model
- Main Theorems
- Global Existence and Exponential Stability in H1
- Global Existence of Solutions in H1
- Exponential Stability of Solutions in H1
- Global Existence and Exponential Stability in H2
- Global Existence of Solutions in H2
- Exponential Stability of Solutions in H2
- Global Existence and Exponential Stability in H4
- Global Existence of Solutions in H4
- Exponential Stability of Solutions in H4
- Bibliographic Comments
- Global Existence, Uniqueness and Exponential Stability of Solutions for the One-Dimensional Navier-Stokes Equations with Capillarity
- Introduction
- Model and Main Results
- Korteweg-Type Model
- Main Theorems
- Global Existence and Exponential Stability in H1+
- Global Existence in H1+
- Asymptotic Behavior in H1+
- Exponential Stability in H1+
- Global Existence and Exponential Stability in H2+
- Global Existence and Uniqueness in H2+
- Exponential Stability in H2+
- Global Existence and Exponential Stability in H4+
- Global Existence in H4+
- Asymptotic Behavior of Solutions in H4+
- Exponential Stability in H4+
- Bibliographic Comments
- Exponential Stability of Solutions for the Compressible p-th Power Newtonian Fluid with Large Initial Data
- Introduction
- Model and Main Results
- Global Existence and Exponential Stability in H1
- Global Existence in H1
- Exponential Stability in H1
- Global Existence and Exponential Stability in H2
- Global Existence and Exponential Stability in H4
- Bibliographic Comments
- Global Existence and Asymptotic Behavior of Spherically Symmetric Solutions for the Multi-Dimensional Infrarelativistic Model
- Introduction
- Reformulation and Main Theorems
- Reformulation of Model
- Main Theorems
- Global Existence and Asymptotic Behavior in H1
- Global Existence in H1
- Asymptotic Behavior in H1
- Global Existence and Asymptotic Behavior in H2
- Global Existence in H2
- Asymptotic Behavior in H2
- Global Existence and Asymptotic Behavior in H4
- Global Existence in H4
- Asymptotic Behavior in H4
- Bibliographic Comments
- Global Existence and Asymptotic Behavior of Cylindrically Symmetric Solutions for the 3D Infrarelativistic Model with Radiation
- Introduction
- Reformation and Main Results
- Reformation of Model
- Main Theorems
- Global Existence and Asymptotic Behavior in H1
- Global Existence in H1
- Asymptotic Behavior in H1
- Global Existence and Asymptotic Behavior in H2
- Global Existence in H2
- Asymptotic Behavior in H2
- Global Existence and Asymptotic Behavior in H4
- Global Existence in H4
- Asymptotic Behavior in H4
- Bibliographic Comments
- Bibliography
