Scattering Map for the Vlasov–Poisson System
Patrick Flynn , Zhimeng Ouyang , Benoit Pausader , Klaus Widmayer
Peking Mathematical Journal ›› 2021, Vol. 6 ›› Issue (2) : 365 -392.
Scattering Map for the Vlasov–Poisson System
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.
Division of Mathematical Sciences(1700282)
EPFL Lausanne
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