等熵可壓縮Navier-Stokes方程解的整體適定性與大時(shí)間性態(tài)
發(fā)布時(shí)間：2020-12-15 17:38
在物理中,Navier-Stokes方程組是以Claude-Louis Navier和 George Gabriel S-tokes命名的,是描述流體介質(zhì)運(yùn)動(dòng)的基本方程。將牛頓第二定律應(yīng)用于流體運(yùn)動(dòng),假設(shè)流體的應(yīng)力項(xiàng)是耗散項(xiàng)（速度的梯度）和壓力之和,那么我們就可以得到該方程。它是描述粘性流體的基本方程。關(guān)于Navier-Stokes方程的重要性,一方面源于它在氣象學(xué),海洋流體力學(xué),繞機(jī)翼空氣流體力學(xué)等方面的廣泛應(yīng)用,另一方面,從純數(shù)學(xué)非線性本身意義上也是極為重要的。本文借助Navier-Stokes方程組,研究了三維無(wú)限區(qū)域內(nèi),氣體的穩(wěn)定性與大時(shí)間的漸近性態(tài)。我們集中討論等熵可壓縮Navier-Stokes方程。文章安排如下：第一章介紹了一些物理背景和相關(guān)的研究進(jìn)展,并介紹了論文中的主要問(wèn)題和方法。第二章,我們研究了一個(gè)無(wú)限拉伸的球內(nèi)可壓縮流光滑解的全局存在性。這是一個(gè)很有趣的問(wèn)題,它涉及到可壓縮Navier-Stokes方程在一個(gè)依賴(lài)時(shí)間的區(qū)域內(nèi),并在時(shí)間趨向無(wú)窮時(shí)會(huì)出現(xiàn)真空情況下的解的性質(zhì)的研究。氣體的運(yùn)動(dòng)被三維等熵可壓縮Navier-Stokes方程描述。從物理的觀點(diǎn)來(lái)看,由于氣...
【文章來(lái)源】：南京大學(xué)江蘇省 211工程院校 985工程院校 教育部直屬院校
【文章頁(yè)數(shù)】：141 頁(yè)
【學(xué)位級(jí)別】：博士
【文章目錄】：
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
致謝
論文情況
本文編號(hào)：2918637
【文章來(lái)源】：南京大學(xué)江蘇省 211工程院校 985工程院校 教育部直屬院校
【文章頁(yè)數(shù)】：141 頁(yè)
【學(xué)位級(jí)別】：博士
【文章目錄】：
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
致謝
論文情況
本文編號(hào)：2918637
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