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Time decay, propagation of low moments and dispersive effects for kinetic equations. (English) Zbl 0852.35139

Summary: We prove time decay estimates for several kinetic equations like the free transport, Boltzmann and Vlasov-Poisson equations. We also consider solutions with infinite energy of the Vlasov-Poisson equation and we show that low moments in the velocity variable are propagated. As a consequence, we prove that the potential energy becomes finite immediately and that the kinetic energy is locally finite. Our approach is based on new dispersive identities for transport equations.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
35Q35 PDEs in connection with fluid mechanics
82C70 Transport processes in time-dependent statistical mechanics
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