等熵可压缩Navier-Stokes方程解的整体适定性与大时间性态
发布时间：2020-12-15 17:38
在物理中,Navier-Stokes方程组是以Claude-Louis Navier和 George Gabriel S-tokes命名的,是描述流体介质运动的基本方程。将牛顿第二定律应用于流体运动,假设流体的应力项是耗散项（速度的梯度）和压力之和,那么我们就可以得到该方程。它是描述粘性流体的基本方程。关于Navier-Stokes方程的重要性,一方面源于它在气象学,海洋流体力学,绕机翼空气流体力学等方面的广泛应用,另一方面,从纯数学非线性本身意义上也是极为重要的。本文借助Navier-Stokes方程组,研究了三维无限区域内,气体的稳定性与大时间的渐近性态。我们集中讨论等熵可压缩Navier-Stokes方程。文章安排如下：第一章介绍了一些物理背景和相关的研究进展,并介绍了论文中的主要问题和方法。第二章,我们研究了一个无限拉伸的球内可压缩流光滑解的全局存在性。这是一个很有趣的问题,它涉及到可压缩Navier-Stokes方程在一个依赖时间的区域内,并在时间趋向无穷时会出现真空情况下的解的性质的研究。气体的运动被三维等熵可压缩Navier-Stokes方程描述。从物理的观点来看,由于气...
【文章来源】：南京大学江苏省 211工程院校 985工程院校 教育部直属院校
【文章页数】：141 页
【学位级别】：博士
【文章目录】：
中文摘要
Abstract
Chapter 1 Preface
1.1 The compressible viscous flow in a 3-D expanded ball
1.2 The compressible viscous flow in partial Space-Periodic Domains
1.3 The compressible flow in the domain between two coaxial cylinders10
Chapter 2 On the global smooth solution to the 3-D compressible Navier-Stokes equation in an infinitely expanded ball 16
2.1 Introduction and main results
2.2 Local existence of the solution to （2.1.1）-（2.1.2） with （2.1.3）
2.3 Some uniform weighted energy estimates for the problem （2.1.1）-（2.1.3） 31
2.4 The uniform global energy estimates for the problem （2.1.1）-（2.1.3）.47
2.5 The proof of Theorem 2.1.1
Chapter 3 Large time asymptotic behavior of the compressible Navier-Stokes Equations in partial Space-Periodic Domains 66
3.1 Introduction and main results
3.2 Some analysis on the homogeneous linearized problem of （3.1.3）
3.3 The global existence of the solution to the auxiliary problem （3.1.7）
2"> 3.4 Some decay properties of the solution u（t, z） to （3.1.3） for z∈T×R2
3.5 Large-time behavior of the solution to （3.1.7） and the proof of Theorem 3.1.1
3.6 The proofs of Theorem 3.1.2 and Theorem 3.1.3
Chapter 4 Stability and Large time behavior of the compressible flow in the domain between two coaxial cylinders 97
4.1 Introduction and main results
4.2 The resolvent problem and the estimates of the lower frequency part
4.3 The proof of Theorem 4.1.1
4.4 The proof of Theorem 4.1.3
Bibliography
致谢
论文情况
本文编号：2918637
【文章来源】：南京大学江苏省 211工程院校 985工程院校 教育部直属院校
【文章页数】：141 页
【学位级别】：博士
【文章目录】：
中文摘要
Abstract
Chapter 1 Preface
1.1 The compressible viscous flow in a 3-D expanded ball
1.2 The compressible viscous flow in partial Space-Periodic Domains
1.3 The compressible flow in the domain between two coaxial cylinders10
Chapter 2 On the global smooth solution to the 3-D compressible Navier-Stokes equation in an infinitely expanded ball 16
2.1 Introduction and main results
2.2 Local existence of the solution to （2.1.1）-（2.1.2） with （2.1.3）
2.3 Some uniform weighted energy estimates for the problem （2.1.1）-（2.1.3） 31
2.4 The uniform global energy estimates for the problem （2.1.1）-（2.1.3）.47
2.5 The proof of Theorem 2.1.1
Chapter 3 Large time asymptotic behavior of the compressible Navier-Stokes Equations in partial Space-Periodic Domains 66
3.1 Introduction and main results
3.2 Some analysis on the homogeneous linearized problem of （3.1.3）
3.3 The global existence of the solution to the auxiliary problem （3.1.7）
2"> 3.4 Some decay properties of the solution u（t, z） to （3.1.3） for z∈T×R2
3.6 The proofs of Theorem 3.1.2 and Theorem 3.1.3
Chapter 4 Stability and Large time behavior of the compressible flow in the domain between two coaxial cylinders 97
4.1 Introduction and main results
4.2 The resolvent problem and the estimates of the lower frequency part
4.3 The proof of Theorem 4.1.1
4.4 The proof of Theorem 4.1.3
Bibliography
致谢
论文情况
本文编号：2918637
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