THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

• Published in: Acta mathematica scientia Vol. 36; no. 4; pp. 1049 - 1097
• Main Author: 王路生 肖清华 熊林杰 赵会江
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-07-2016; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China; Department of Mathematics, Northwest University, Xi'an 710127, China%Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China%College of Mathematics and Econometrics, Hunan University, Changsha 410082, China%School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
• Subjects: 35Q20; 35Q83; 65M99; 78A35; Cauchy problem; Collision dynamics; Construction; global solutions near Maxwellians; Kernels; long-range interactions; Mathematical models; One-species Vlasov-Poisson-Boltzmann system; Perturbation methods; time-velocity weighted energy method; 中性条件; 分子间; 初始扰动; 排斥势; 柯西问题; 碰撞; 系统; 长程相互作用; 78A35; global solutions near Maxwellians; One-species Vlasov-Poisson-Boltzmann system; 35Q20; time-velocity weighted energy method; 65M99; 35Q83; long-range interactions
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(16)30057-1

In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in [12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.