On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potentialReport as inadecuate




On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential - Download this document for free, or read online. Document in PDF available to download.

1 LMJL - Laboratoire de Mathématiques Jean Leray 2 IECL - Institut Élie Cartan de Lorraine

Abstract : We prove a global existence result with initial data of low regularity, and prove the trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with small non linear term but with a possibly large exterior confining potential in dimension $d=2$ and $d=3$. The proof relies on a fixed point argument using sharp estimates at short and long time scales of the semi-group associated to the Fokker-Planck operator, which were obtained by the first author.

Keywords : global solutions return to equilibrium Vlasov-Poisson-Fokker-Planck equation non self-adjoint operator





Author: Frédéric Hérau - Laurent Thomann -

Source: https://hal.archives-ouvertes.fr/



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