arXiv subjects

G. Velo

Publications and source records attributed to G. Velo.

21 records · Page 2Linked to original sources

arXiv1999

Long Range Scattering and Modified Wave Operators for some Hartree Type Equations II

We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma}. For 0 < gamma < or =1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators,thereby extending the results of a previous paper with the same title (math.AP/9807031) which covered the range 1/2 < gamma <1.

math.AP↗

arXiv1998

Scattering Theory in the Energy Space for a Class of Hartree Equations

We study the theory of scattering in the energy space for the Hartree equation in space dimension n>2. Using the method of Morawetz and Strauss, we prove in particular asymptotic completeness for radial nonnegative nonincreasing potentials satisfying suitable regularity properties at the origin and suitable decay properties at infinity. The results cover in particular the case of the potential |x|^(- gamma) for 2 < gamma < Min(4,n).

math.AP↗

arXiv1998

Long Range Scattering and Modified Wave Operators for some Hartree Type Equations

We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.

math.AP↗