arXiv:2007.16025 Abstract | arXiv Analytics

arXiv:2007.16025 [math.AP]Abstract References Reviews Resources

Mean-field limits: from particle descriptions to macroscopic equations

Published 2020-07-31Version 1

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.

Categories: math.AP

Keywords: macroscopic equations, mean-field limits, derive pressureless euler-type equations, nonlocal velocity fields, newton-type particle descriptions

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