论文标题
具有松弛的非本地欧拉系统中的临界阈值
Critical thresholds in a nonlocal Euler system with relaxation
论文作者
论文摘要
我们提出和研究具有松弛的非局部欧拉系统，该系统倾向于在双曲线缩放率极限下严格屈曲系统。任何空间维度都介绍了该系统的局部存在和独特性的独立证明。我们在一维设置中进一步得出了该系统的确切关键阈值。我们的结果表明，这种非局部系统可以接受大量初始数据的全局平滑解决方案。因此，非局部速度将无效的Euler系统中的通用有限时间分解规范化。
We propose and study a nonlocal Euler system with relaxation, which tends to a strictly hyperbolic system under the hyperbolic scaling limit. An independent proof of the local existence and uniqueness of this system is presented in any spatial dimension. We further derive a precise critical threshold for this system in one dimensional setting. Our result reveals that such nonlocal system admits global smooth solutions for a large class of initial data. Thus, the nonlocal velocity regularizes the generic finite-time breakdown in the pressureless Euler system.
