We study an asymptotic limit of Vlasov type equation with nonlocal interaction forces where the friction terms are dominant. We provide a quantitative estimate of this large friction limit from the kinetic equation to a continuity type equation with a nonlocal velocity field, the so-called aggregation equation, by employing 2-Wasserstein distance. By introducing an intermediate system, given by the pressureless Euler equations with nonlocal forces, we can quantify the error between the spatial densities of the kinetic equation and the pressureless Euler system by means of relative entropy type arguments combined with the 2-Wasserstein distance. This together with the quantitative error estimate between the pressureless Euler system and the aggregation equation in 2-Wasserstein distance in [Commun. Math. Phys, 365, (2019), 329–361] establishes the quantitative bounds on the error between the kinetic equation and the aggregation equation.

我们研究了具有非局部相互作用力且摩擦项占主导地位的Vlasov型方程的渐近极限。通过使用2-Wasserstein距离，我们可以从动力学方程到具有非局部速度场的连续性方程，即所谓的聚集方程，对这种较大的摩擦极限进行定量估计。通过引入由具有非局部力的无压力欧拉方程给出的中间系统，我们可以通过相对熵类型自变量结合2-Wasserstein距离来量化动力学方程和无压力欧拉系统的空间密度之间的误差。这与无压力的欧拉系统和2-Wasserstein距离中的聚集方程之间的定量误差估计一起使用。数学。物理，365，（2019），