Global Regularity for 1D Eulerian Dynamics with Singular Interaction Forces
Global Regularity for 1D Eulerian Dynamics with Singular Interaction Forces
复制标题
DOI：
10.1137/17m1141515
复制
发表时间：
2017-07
期刊：
影响因子：
--
通讯作者：
A. Kiselev;Changhui Tan
中科院分区：
文献类型：
--
作者：
A. Kiselev;Changhui Tan
Euler-Poisson-Alignment（EPA）系统出现在数学生物学中，用于在流体动力学极限下对一组通过相互吸引/排斥以及对齐力相互作用的代理进行建模。我们考虑一类具有奇异排列项和自然吸引/排斥项的一维EPA系统。对齐核的奇异性产生了一个有趣的效果，使方程的解正则化，并导致大范围的初始数据的全局正则性。这是最近由Do、Kiselev、Ryzhik和Tan在论文中观察到的。本文的目标是推广这个结果并引入吸引/排斥势。我们证明了这些更一般的模型的全局正则性。
The Euler-Poisson-Alignment (EPA) system appears in mathematical biology and is used to model, in a hydrodynamic limit, a set agents interacting through mutual attraction/repulsion as well as alignment forces. We consider one-dimensional EPA system with a class of singular alignment terms as well as natural attraction/repulsion terms. The singularity of the alignment kernel produces an interesting effect regularizing the solutions of the equation and leading to global regularity for wide range of initial data. This was recently observed in the paper by Do, Kiselev, Ryzhik and Tan. Our goal in this paper is to generalize the result and to incorporate the attractive/repulsive potential. We prove that global regularity persists for these more general models.