论文标题
平均场限制：从粒子描述到宏观方程
Mean-field limits: from particle descriptions to macroscopic equations
论文作者
论文摘要
我们严格地在速度和聚集方程中具有非局部耗散术语的无压力Euler型方程，并从牛顿型粒子描述中具有与对齐相互作用的牛群模型的非局部速度场。我们至关重要的是，由于非局部相互作用，我们将调制动能的离散版与有限的Lipschitz距离一起进行措施，以在其时间导数中控制术语。
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.
