剪切颗粒气体的Chapman-Enskog展开收敛吗？
Does the Chapman--Enskog expansion for sheared granular gases converge?
摘要：
本文讨论的基本问题是，对于非弹性硬球气体，切应力的部分Chapman-Enskog展开式$P_{xy}=-\sum_{k=0}^\infty η_k ({\partial u_x}/{\partial y})^{2k+1}$是否收敛。通过使用一个简单的动力学模型，它表明，在相反的弹性情况下，上述系列收敛，收敛半径增加与非弹性。有人认为，这一矛盾的结论是不是一个人工制品的动力学模型，可以理解的时间演变的缩放剪切速率在均匀剪切流。
英文摘要：
The fundamental question addressed in this paper is whether the partial Chapman--Enskog expansion $P_{xy}=-\sum_{k=0}^\infty η_k ({\partial u_x}/{\partial y})^{2k+1}$ of the shear stress converges or not for a gas of inelastic hard spheres. By using a simple kinetic model it is shown that, in contrast to the elastic case, the above series does converge, the radius of convergence increasing with inelasticity. It is argued that this paradoxical conclusion is not an artifact of the kinetic model and can be understood in terms of the time evolution of the scaled shear rate in the uniform shear flow.
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