The Vlasov equation cannot fully account for collisionless shocks
arXiv:2506.01548
Abstract
It is argued that the Vlasov equation cannot fully account for collisionless shocks since it conserves entropy, while a shock does not. A rigorous mathematical theory of collisionless shocks could require working at the Klimontovich level.
6 pages, 1 figure, to appear in Contributions to Plasma Physics