Scattering map for the Vlasov-Poisson system. (English) Zbl 1519.35324
Summary: We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as \(t\rightarrow -\infty\) to asymptotic dynamics as \(t\rightarrow +\infty\). The main novelty is the construction of modified wave operators, but we also obtain a new simple proof of modified scattering. Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system. Via a pseudo-conformal inversion, we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.
MSC:
| 35Q83 | Vlasov equations |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35P25 | Scattering theory for PDEs |
| 78A35 | Motion of charged particles |
| 82D10 | Statistical mechanics of plasmas |
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