Heteroclinic orbits for the nonlinear Vlasov and the one-dimensional Vlasov–Poisson systems. (October 2019)

• Record Type: Journal Article
• Authors: Binshati, Ismahan; Tudorascu, Adrian
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 180
• Page End: 204
• Publication Date: 2019-10
• Subjects: Nonlinear Vlasov system -- Vlasov–Poisson system -- Heteroclinic orbits -- Wasserstein distance; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.04.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove existence of heteroclinic orbits for the nonlinear Vlasov and the one-dimensional Vlasov–Poisson systems. In the nonlinear Vlasov case with sufficiently regular and periodic potential we show that there is at least one orbit emanating from a maximum point of the potential and at least one terminating at it. The Vlasov–Poisson case is more delicate due to the singularity of the potential, and our existence result is limited to one spatial dimension and to weak solutions in the space of probability measures on the torus endowed with the periodic Wasserstein distance.