带阻尼项的可压缩欧拉方程组的经典解-应用数学专业论文.docxVIP

Abstract Abstract II II THE CLASSICAL SOLUTIONS OF THE COMPRESSIBLE EULER EQUATIONS WITH DAMPING ABSTRACT Euler equations is an important part of the nonlinear partial differential equations. Especially, the Euler equations with damping has been one of the most active research fields in nonlinear partial differential equations. The aim of this thesis is to research the classical solutions of the Euler equations with damping. Results obtained in this thesis improve and extend many existing results. Full-text is divided into five chapters: Firstly, we introduce the research background and the research status of the Euler equations with damping. Moreover, the main work of this thesis is described. Secondly, blowup for the solutions of the Euler equations with damping in n-dimensional space is discussed by structuring precise spherically symmetric solutions u ??c ?t ??x????. Furthermore, blowup for the radially symmetric solutions of the Euler equations with damping in n-dimensional space is studied via the integration method. Then, the global existence and blowup for the rotated solutions consisting of some basic functions of a class of Euler equations in 3-dimensional space is investigated. As an extensive generalization, the high order estimation for the solutions of a class of Euler equations with damping in 1-dimensional space is analyzed. At last, the main works and future works of this thesis are stated. Key Words: Euler equations, Damping, Spherically symmetric solutions, Radially symmetric solutions, Rotated solutions, Blowup 目录 目录 III III 目录 HYPERLINK \l _bookmark0 第一章 绪论 1 HYPERLINK \l _bookmark1 1.1 HYPERLINK \l _bookmark1 研究背景和研究动机 1 HYPERLINK \l _bookmark2 1.2 HYPERLINK \l _bookmark2 论文结构及主要内容 1 HYPERLINK \l _bookmark3 第二章 带阻尼项的欧拉方程组的球形对称解的爆破性质 4 HYPERLINK \l _bookmark4 2.1 HYPERLINK \l _bookmark4 欧拉方程组球形对称解的研究现状 4 HYPERLINK \l _bookmark5 2.2 HYPERLINK \l _bookmark5 主要结果 5 HYPERLINK \l _bookmark6 第三章 带阻尼项的欧拉方程组的径向对称解的爆破性质 12