The hydrodynamical limit of the Vlasov-Poisson system. (English) Zbl 1016.82026
Two models are considered for an ensemble of particles with selfconsistent interaction when examining the time evolution of the kinetic and fluid model provided by the Vlasov-Poisson system, and the Euler-Poisson system with zero pressure. It is shown that if the kinetic description of the velocities concentrates, then the velocities also concentrate at some subsequent time. It is then shown that in the hydrodynamical limit this concentration represents a solution of the fluid dynamical model.
Reviewer: A.Jeffrey (Newcastle upon Tyne)
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76F99 | Turbulence |
Keywords:
kinetic model; Vlasov-Poisson system; Euler-Poisson system; zero pressure; hydrodynamcial limit; fluid dynamical modelReferences:
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