Global weak solutions for the Vlasov–Poisson system with a point charge. (21st October 2014)

• Record Type: Journal Article
• Authors: Chen, Jing; Zhang, Xianwen; Wei, Jinbo
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 3776
• Page End: 3791
• Publication Date: 2014-10-21
• Subjects: Vlasov–Poisson system -- point charge -- attractive interaction -- weak solution -- global existence; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3316
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We study the dynamics of three‐dimensional Vlasov‐Poisson system in the presence of a point charge with attractive interaction. Compared to the repulsive interaction, we cannot get a priori conversation law. Nevertheless, we are able to obtain bound of kinetic energy by introducing a Lyapunov functional. Combining this result with the concept of Diperna‐Lions flow, we establish global existence of weak solutions for this system. Copyright © 2014 John Wiley & Sons, Ltd.