带外场的空间非均匀Boltzmann方程的一致L~p稳定性
发布时间：2018-12-13 13:45
【摘要】：Boltzmann方程是一类重要的微分方程,它的数学理论研究也一直是最具有挑战的研究领域之一,特别是解的性质研究.本文是在初值f0充分小且关于多项式或指数央速衰减的条件下,研究带一种外力场且具有角截断的逆幂位势的Boltzmann方程温和解的稳定性问题,包括部分软位势和Maxwellian模型(-4/37≤0)、硬位势和硬求模型(0γ≤1).在此之前,Duan-Yang-Zhu在2005年的文章中已经给出了特征方程的解满足一定条件时Boltzmann方程温和解的全局存在性,而本文是在此条件的基础上又给外力作了一个限制(即(?)0∞||E(t)||Lx∞dt≤C0),来得到温和解的稳定性.本文的主要证明思路来源于Ha-Lee-Yun 2009年的文章,但它证明的是带有小外力场空间非均匀Boltzamnn经典解的稳定性,本文的外力场与之相比较要“大”些,而且在硬位势和硬球模型情形下,指数衰减指标可以优化到λ2ε0,这里的ε可以充分小.首先是对温和解的加权Lp范数作估计(权重是(1+|u|2)k/2),得到当p3时关于时间t的可积性,然后再对初值分别为f0和f0的Boltzmann方程温和解差的加权Lp范数关于时间t的导数作估计,最后利用Gronwall型不等式.就可以得到稳定性的证明,其中硬位势和硬球模型情形下利用的是一种广义的Gronwall不等式.
[Abstract]:Boltzmann equation is a kind of important differential equation, its mathematical theory research is one of the most challenging research fields, especially the study of the properties of solution. In this paper, under the condition that the initial value f _ 0 is sufficiently small and the polynomial or exponential central velocity is attenuated, the temperature and stability of the Boltzmann equation with an external force field and an inverse power potential with angular truncation are studied. It includes partial soft potential and Maxwellian model (-4 / 37 鈮，
本文编号：2376633
[Abstract]:Boltzmann equation is a kind of important differential equation, its mathematical theory research is one of the most challenging research fields, especially the study of the properties of solution. In this paper, under the condition that the initial value f _ 0 is sufficiently small and the polynomial or exponential central velocity is attenuated, the temperature and stability of the Boltzmann equation with an external force field and an inverse power potential with angular truncation are studied. It includes partial soft potential and Maxwellian model (-4 / 37 鈮，
本文编号：2376633
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