Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off
We consider a N-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like N−δ with δ<1/d in the force, we provide...
| Main Authors: | , , |
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| Format: | Journal article |
| Published: |
World Scientific Publishing
2018
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| Summary: | We consider a N-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like N−δ with δ<1/d in the force, we provide a quantitative error estimate between the empirical measure associated to that N-particle system and the solutions of the d-dimensional Vlasov–Poisson–Fokker–Planck (VPFP) system. We also study the propagation of chaos for the Vlasov–Fokker–Planck equation with less singular interaction forces than the Newtonian one. |
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