带有非局部效应耦合流体模型的局部经典解

The Local Classical Solution of Coupled Fluid Model with Nonlocal Effect

本文研究了带有非局部速度趋同效应的耦合模型。该系统通过阻尼项对粒子速度和流体速度进行耦合,描述了群集粒子在粘性不可压流体中的相互作用。本文首先构造逼近方程和逼近解,并应用能量估计的方法,得到逼近解的一致先验估计,然后利用低阶范数收敛,证明具有非局部速度趋同效应的欧拉系统局部解的存在唯一性。

This paper studied a coupling model with non-local velocity alignment. In this system, particle ve-locity and fluid velocity are coupled by damping term, and the interaction of cluster particles in viscous incompressible fluid is described. We first construct the approximation equation and the approximation solution, and the uniform a priori estimate of the approximation solution is obtained by using the method of energy coupling estimation, and then the existence and uniqueness of the local solution of the Euler system with non-local velocity convergence effect is proved by using the lower-order norm convergence.