L 1 STABILITY FOR THE VLASOV–POISSON–BOLTZMANN SYSTEM AROUND VACUUM
RENJUN DUAN, MEI ZHANG, CHANGJIANG ZHU
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Source: Crossref
Published: Sep 1, 2006
DOI: 10.1142/s0218202506001613
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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 L 1 stability 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 L 1 stability is also obtained for the case of N = 3.
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