论文标题
一维约束欧拉方程的软拥塞近似
Soft congestion approximation to the one-dimensional constrained Euler equations
论文作者
论文摘要
本文涉及对具有奇异压力定律的一维压缩欧拉方程的分析，即所谓的硬球方程。结果是双重的。首先，我们通过粘性正则化和精致的补偿紧凑性论证来确定有限的弱解决方案的存在。其次，我们通过提供奇异压力对解决方案分解的影响的详细描述来研究平滑设置。在这个平滑的框架中，我们严格地证明了对自由质量的Euler方程的奇异限制，在该方程中，可压缩（自由）动力学与受约束（交通拥堵的）域中不可压缩的动力学结合。
This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded weak solutions by means of a viscous regularization and refined compensated compactness arguments. Second, we investigate the smooth setting by providing a detailed description of the impact of the singular pressure on the breakdown of the solutions. In this smooth framework, we rigorously justify the singular limit towards the free-congested Euler equations, where the compressible (free) dynamics is coupled with the incompressible one in the constrained (i.e. congested) domain.
