28 Pages
English
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Mean field limit for interacting particles

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28 Pages
English

Description

Mean field limit for interacting particles P-E Jabin (University of Nice) Joint works with J. Barre and M. Hauray

  • diperna-lions

  • formal limit

  • initial condition

  • lions-perthame

  • corresponding initial

  • unique solution

  • fn

  • coulomb potential

  • fact lipschitz


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naeMfieldlimitforinteractingparticlesP-EJabin(UniversityofJointworkswithJ.Barre´and)eciNM.Hauray
nIetartcnigaptrilcseConsiderNparticles,identicalandinteractingtwobytwothroughthekernelK.DenoteXi(t)ΠdandVi(t)Rdthepositionandvelocityofthei-thparticle.Then1ddXdtXi=Vi,dtVi=NK(XiXj).i=6jTheN1isarenormalizationtogetthecorrecttimescale.ThemostimportantcaseisCoulombinteractionαK(x)=−rΦ,Φ(x)=|x|d2+regular.Thecaseα>0correspondstotherepulsive/electrostaticcase(plasmas...)andα<0totheattractive/gravitationalcase(cosmology...).tOehreknreslfonietersteixtsohewev.r..(1)