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5 papers · 2 filters
Scattering map for the Vlasov-Maxwell system around source-free electromagnetic fields
Léo Bigorgne
We construct an isometric modified scattering operator, mapping any sufficiently regular past scattering state, with a small distribution function, to the future one corresponding…
Low regularity solutions to the logarithmic Schrodinger equation
Rémi Carles, Masayuki Hayashi, Tohru Ozawa
We consider the logarithmic Schr{ö}dinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H^1 to L^2 , and that this extension is L…
Modified scattering of small data solutions to the Vlasov-Poisson system with a trapping potential
Léo Bigorgne, Anibal Velozo Ruiz, Renato Velozo Ruiz
In this paper, we study small data solutions to the Vlasov-Poisson system with the simplest external potential, for which unstable trapping holds for the associated Hamiltonian flo…
On nonlinear effects in multiphase WKB analysis for the nonlinear Schrodinger equation
Remi Carles
We consider the Schrodinger equation with an external potential and a cubic nonlinearity, in the semiclassical limit. The initial data are sums of WKB states, with smooth phases an…
Pathological set with loss of regularity for nonlinear Schr{ö}dinger equations
Rémi Carles, Louise Gassot
We consider the mass-supercritical, defocusing, nonlinear Schr{ö}dinger equation. We prove loss of regularity in arbitrarily short times for regularized initial data belonging to a…