论文标题
碰撞统治方面的同型解决方案的长期行为，用于硬势
Longtime behavior for homoenergetic solutions in the collision dominated regime for hard potentials
论文作者
论文摘要
在本文中，我们考虑了Boltzmann方程的特定类别解决方案，该解决方案称为同型解决方案。他们描述了由于碰撞而引起的稀释气的动力学以及剪切，扩张或两者组合的作用。我们证明，最初具有高温的解决方案保持接近并收敛到麦克斯韦分布，温度将变为无穷大。此外，我们为温度提供精确的渐近公式。这种局部稳定性结果是相对速度相对于相对速度的主要剪切和均匀性$γ> 0 $的结果。证明依赖于由希尔伯特型扩张所激发的安萨兹。我们考虑非切割和截止内核。
In this paper, we consider a particular class of solutions to the Boltzmann equation which are referred to as homoenergetic solutions. They describe the dynamics of a dilute gas due to collisions and the action of either a shear, a dilation or a combination of both. We prove that solutions with initially high temperature remain close and converge to a Maxwellian distribution with temperature going to infinity. Furthermore, we give precise asymptotic formulas for the temperature. This local stability result is a consequence of a dominant shear and the homogeneity $ γ>0 $ of the collision operator with respect to relative velocities. The proof relies on an ansatz which is motivated by a Hilbert-type expansion. We consider both non-cutoff and cutoff kernels.
