L1STABILITY FOR THE VLASOV–POISSON–BOLTZMANN SYSTEM AROUND VACUUM

Author:

DUAN RENJUN1,ZHANG MEI2,ZHU CHANGJIANG2

Affiliation:

1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, P. R. China

2. Laboratory of Nonlinear Analysis, Department of Mathematics, Huazhong Normal University, Wuhan 430079, P. R. China

Abstract

Based on the global existence theory of the Vlasov–Poisson–Boltzmann system around vacuum in the N-dimensional phase space, in this paper, we prove the uniform L1stability of classical solutions for small initial data when N ≥ 4. In particular, we show that the stability can be established directly for the soft potentials, while for the hard potentials and hard sphere model it is obtained through the construction of some nonlinear functionals. These functionals thus generalize those constructed by Ha for the case without force to capture the effect of the force term on the time evolution of solutions. In addition, the local-in-time L1stability is also obtained for the case of N = 3.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

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