论文标题
关于恩斯科方程的独特性和稳定性
On uniqueness and stability for the Enskog equation
论文作者
论文摘要
真空中中等密度的气体在经典力学中通过从Enskog方程获得的粒子密度函数描述。基于跳跃的McKean-Vlasov随机方程，最近在\ cite {ars17}中研究了相关的随机过程。后者的工作在\ cite {frs18}中扩展到没有毕业生的角度截止假设的一般硬势和软势的情况。通过引入移动距离，该距离准确补偿了在空间不均匀环境中产生的自由运输项，我们在这项工作中证明了Wasserstein距离的不平等，对于恩斯科方方程的任何两个测量值增值溶液。特别的结果，我们发现了足够的条件，可以实现适用于无角临界值的硬质和软势的enskog方程解决方案的唯一性和连续依赖性。
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Enskog equation. Based on a McKean-Vlasov stochastic equation with jumps, the associated stochastic process was recently studied in \cite{ARS17}. The latter work was extended in \cite{FRS18} to the case of general hard and soft potentials without Grad's angular cut-off assumption. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measure-valued solutions to the Enskog equation. As a particular consequence, we find sufficient conditions for the uniqueness and continuous-dependence on initial data for solutions to the Enskog equation applicable to hard and soft potentials without angular cut-off.
