DiPerna, R. J.; Lions, Pierre-Louis Global weak solutions of kinetic equations. (English) Zbl 0813.35087 Rend. Semin. Mat., Torino 46, No. 3, 259-288 (1988). This paper is a unified review of some results of the authors recently published. They deal with the existence and various properties of weak solutions of kinetic equations. The presentation includes Boltzmann, Vlasov-Poisson, Vlasov-Maxwell, Fokker-Planck equations. The various notions of solutions are explained, existence and stability results are given and the main ingredients of the proofs are outlined. Reviewer: F.Rosso (Firenze) Cited in 16 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:review of recent results; Boltzmann; Vlasov-Poisson; Vlasov-Maxwell; Fokker-Planck equations PDF BibTeX XML Cite \textit{R. J. DiPerna} and \textit{P.-L. Lions}, Rend. Semin. Mat., Torino 46, No. 3, 259--288 (1988; Zbl 0813.35087) OpenURL