Fluid-Dynamic Limit for the Centered Rarefaction Wave of the Broadwell Equation
Fluid-Dynamic Limit for the Centered Rarefaction Wave of the Broadwell Equation
复制标题
DOI：
10.1006/jdeq.1998.3488
复制
发表时间：
1998-12
影响因子：
2.4
通讯作者：
Wei-Cheng Wang;Z. Xin
中科院分区：
文献类型：
--
作者：
Wei-Cheng Wang;Z. Xin
本文研究了在小平均自由程极限下，一维非线性Boltzmann方程的Broadwell模型与相应的可压缩气体动力学Euler方程的渐近等价性，考虑了允许初始数据具有跳跃间断，使得相应的Euler方程的解包含中心稀疏波的情形。特别是，包括由稀疏曲线连接的黎曼数据。我们表明，只要初始数据是一个小扰动的非真空恒定状态，Broadwell方程的解决方案存在于全球的时间和收敛，在小的平均自由程限制，相应的欧拉方程的解决方案一致，除了初始层的宽度基本上是平均自由程的顺序。
Abstract We study the asymptotic equivalence of the 1-d Broadwell model of the nonlinear Boltzmann equation to its corresponding Euler equation of compressible gas dynamics in the limit of small mean free path. We consider the case where the initial data are allowed to have jump discontinuities such that the corresponding solutions to the Euler equation contain centered rarefaction waves. In particular, Riemann data connected by rarefaction curves are included. We show that, as long as the initial data are a small perturbation of a non-vacuum constant state, the solution for the Broadwell equation exists globally in time and converges, in the small mean free path limit, to the solution of the corresponding Euler equation uniformly except for an initial layer whose width is essentially the order of the mean free path.