平均场极限：从粒子描述到宏观方程
Mean-field limits: from particle descriptions to macroscopic equations
摘要：
我们严格推导出无压欧拉型方程的非局部耗散项的速度和聚集方程的非局部速度场的牛顿型粒子描述的群集模型与对齐的相互作用。我们至关重要的是利用一个离散版本的调制动能与有界Lipschitz距离的措施，以控制其时间导数由于非局部相互作用的条款。
英文摘要：
We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. We crucially make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.
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