一类弱耗散的二分量μ-Hunter-Saxton方程组的整体弱解存在性

发布时间：2019-01-06 06:50

【摘要】：本文主要研究一类弱耗散的二分量μ-Hunter-Saxton方程组弱解的整体存在性问题,首先,对初值进行磨光,并利用这列初始值获得一列整体强解.最后,利用紧性方法获得这类弱耗散的二分量μ-Hunter-Saxton方程组弱解的整体存在性.本文的主要工作如下：1.第一章,简要介绍μ-Hunter-Saxton方程组相关问题的研究发展概况以及本文研究的主要问题.2.第二章,首先,对方程组进行变形.利用算子和格林公式变形分别得到两个方程组.然后,利用Kato's理论得到方程组的局部适定性.最后,针对μ-Hunter-Saxton方程组进行先验估计.3.第三章,首先,我们介绍磨光算子的定义以及一些基本性质.然后,对初值进行磨光,从而得到原方程组的一组逼近解.最后,利用在第二章中得到的估计,我们对逼近解给出进一步的估计.4.第四章,首先,我们利用第二和第三章做的基本能量估计证明逼近解的弱紧性.证明方程组弱解的整体存在性.
[Abstract]:In this paper, we study the global existence of weak solutions for a class of weakly dissipative two-component 渭-Hunter-Saxton equations. Firstly, we polish the initial values and obtain a series of global strong solutions by using the initial values. Finally, by using the compactness method, the global existence of weak solutions for this class of weakly dissipative two-component 渭-Hunter-Saxton equations is obtained. The main work of this paper is as follows: 1. The first chapter briefly introduces the research and development of 渭-Hunter-Saxton equations and the main problems in this paper. 2. In the second chapter, first of all, we deform the equations. By using operator and Green's formula, two equations are obtained, respectively. Then, by using Kato's 's theory, the local fitness of the equations is obtained. Finally, a priori estimate of 渭-Hunter-Saxton equations is given. In the third chapter, we introduce the definition of polishing operator and some basic properties. Then, the initial values are polished and a set of approximate solutions of the original equations are obtained. Finally, using the estimate obtained in Chapter 2, we give a further estimate of the approximate solution. 4. 4. In chapter 4, we first prove the weakly compactness of the approximate solution by using the basic energy estimates given in the second and third chapters. The global existence of weak solutions for equations is proved.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

【相似文献】