Modified scattering for the Vlasov-Poisson system

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We study the asymptotic behavior of dispersing solutions to the Vlasov-Poisson system. Due to long interaction range, we do not expect linear scattering (Choi S-H and Ha S-Y 2011 SIAM J. Math. Anal. 43 2050-77). Instead, we prove a modified scattering result (or long range scattering result) of small and dispersing solutions. We find a quasi-free forward trajectory so that along the trajectory, the solution has an asymptotic limit. We extract the logarithmic growth part of the Duhamel term, and absorb it into the quasi-free trajectory, then the remaining part enjoys faster decay so as to obtain the asymptotic state
Publisher
IOP PUBLISHING LTD
Issue Date
2016-09
Language
English
Article Type
Article
Keywords

LONG-RANGE SCATTERING; NONLINEAR SCHRODINGER-EQUATIONS; SYMMETRIC-SOLUTIONS; HARTREE-EQUATIONS; GLOBAL EXISTENCE; SPACE DIMENSION; INITIAL DATA; REGULARITY; STABILITY

Citation

NONLINEARITY, v.29, no.9, pp.2755 - 2774

ISSN
0951-7715
DOI
10.1088/0951-7715/29/9/2755
URI
http://hdl.handle.net/10203/213783
Appears in Collection
MA-Journal Papers(저널논문)
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