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Renormalized solutions to the Vlasov equation with coefficients of bounded variation. (English) Zbl 0979.35032
This paper deals with the classical Vlasov equation \[ \partial_tu+\xi\nabla_x u+\text{div}_\xi[E(t,x)u]=0,\tag{1} \] which describes the evolution on phase space of the density \(u\) of particles satisfying the fundamental law of mechanics \[ \dot x=\xi,\quad \dot \xi=E(t,x).\tag{2} \] The author proves that weak bounded solutions of (1) with bounded variation coefficients have the renormalization property. Moreover, he shows that when the renormalization property holds for a general transport equation, it also holds for only Lipschitz nonlinearities.

MSC:
35F05 Linear first-order PDEs
82B28 Renormalization group methods in equilibrium statistical mechanics
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