Mean field limit for interacting particles

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

Sujets

• Initial value problem
• Electric potential

Informations

• Publié par: pefav
• Nombre de lectures: 7
• Langue: English

Extrait

naeMfieldlimitforinteractingparticles P-EJabin(Universityof JointworkswithJ.Barre´and )eciN M.Hauray

nIetartcnigaptrilcse ConsiderNparticles,identicalandinteractingtwobytwothrough thekernelK.DenoteX i (t) ∈ Π d andV i (t) ∈ R d thepositionand velocityofthei-thparticle.Then 1dd X dt X i =V i , dt V i = N K(X i − X j ). i= 6 j The N 1 isarenormalizationtogetthecorrecttimescale. ThemostimportantcaseisCoulombinteraction α K(x)= −r Φ,Φ(x)= | x | d − 2 +regular. Thecaseα>0correspondstotherepulsive/electrostaticcase (plasmas...)andα<0totheattractive/gravitationalcase (cosmology...). tOehreknreslfonietersteixtsohewev.r.. (1)