31 citations · 99 across the 23 of their papers we have counts for
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Modified wave operators without loss of regularity for some long range Hartree equations. II
J. Ginibre, G. Velo
We continue the study of the theory of scattering for some long range Hartree equations with potential |x|^-gamma, performed in a previous paper, denoted as I, in the range 1/2 < g…
Modified wave operators without loss of regularity for some long range Hartree equations. I
J. Ginibre, G. Velo
We reconsider the theory of scattering for some long range Hartree equations with potential |x|^-gamma with 1/2 < gamma < 1. More precisely we study the local Cauchy problem with i…
Long range scattering for the Wave-Schrödinger system revisited
Jean Ginibre, Giorgio Velo
We reconsider the theory of scattering for the Wave-Schrödinger system and more precisely the local Cauchy problem with infinite initial time, which is the main step in the constru…
Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schr"odinger and Hartree equations
J. Ginibre, G. Velo
Recently several authors have developed multilinear and in particular quadratic extensions of the classical Morawetz inequality. Those extensions provide (among other results) an e…
Long range scattering for the Maxwell-Schr"odinger system with arbitrarily large asymptotic data
J. Ginibre, G. Velo
We review the proof of existence and uniqueness of solutions of the Maxwell-Schr"odinger system in a neighborhood of infinity in time, with prescribed asymptotic behaviour defined…
Uniqueness at infinity in time for the Maxwell-Schr"odinger system with arbitrarily large asymptotic data
J. Ginibre, G. Velo
We prove the uniqueness of solutions of the Maxwell-Schr"odinger system with given asymptotic behaviour at infinity in time. The assumptions include suitable restrictions on the gr…
Long Range Scattering for the Modified Schr"odinger Map in two space dimensions
J. Ginibre, G. Velo
We study the asymptotic behaviour in time of solutions and the theory of scattering for the modified Schr"odinger map in two space dimensions. We solve the Cauchy problem with larg…
Long Range Scattering and Modified Wave Operators for the Maxwell-Schr"odinger System II. The general case
J. Ginibre, G. Velo
We study the theory of scattering for the Maxwell-Schr"odinger system in space dimension 3, in the Coulomb gauge. We prove the existence of modified wave operators for that system…
Scattering theory for the Zakharov system
J. Ginibre, G. Velo
We study the theory of scattering for the Zakharov system in space dimension 3. We prove in particular the existence of wave operators for that system with no size restriction on t…
Long Range Scattering and Modified Wave Operators for the Wave-Schr"odinger System III
J. Ginibre, G. Velo
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In previous pa…
Long range scattering for some Schr"odinger related nonlinear systems
J. Ginibre, G. Velo
We review some recent results on the theory of scattering and more precisely on the local Cauchy problem at infinity in time for some long range nonlinear systems including some fo…
Long range scattering for the Wave-Schr"odinger system with large wave data and small Schr"odinger data
J. Ginibre, G. Velo
We study the theory of scattering for the Wave-Schr"odinger system with Yukawa type coupling in space dimension 3. We prove in particular the existence of modified wave operators f…
Long range scattering for the Maxwell-Schr"odinger system with large magnetic field data and small Schr"odinger data
J. Ginibre, G. Velo
We study the theory of scattering for the Maxwell-Schr"odinger system in the Coulomb gauge in space dimension 3. We prove in particular the existence of modified wave operators for…
Scattering Theory for the Schr"odinger Equation in some external time dependent magnetic fields
J. Ginibre, G. Velo
We study the theory of scattering for a Schr"odinger equation in an external time dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential…
Long Range Scattering and Modified Wave Operators for the Wave-Schr"odinger system II
J. Ginibre, G. Velo
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous…
Long Range Scattering and Modified Wave Operators for the Maxwell-Schr"odinger system I.The case of vanishing asymptotic magnetic field
J. Ginibre, G. Velo
We study the theory of scattering for the Maxwell-Schr"odinger system in space dimension 3,in the Coulomb gauge.In the special case of vanishing asymptotic magnetic field,we prove…
Long Range Scattering and Modified Wave Operators for the Wave-Schr"odinger system
J. Ginibre, G. Velo
We study the theory of scattering for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling,in space dimension 3.We prove in particular t…
Long Range Scattering and Modified Wave Operators for some Hartree Type Equations III. Gevrey spaces and low dimensions
J. Ginibre, G. Velo
We study the theory of scattering for a class of Hartree type equations with long range interactions in arbitrary space dimension n > or = 1, including the case of Hartree equation…
Long Range Scattering and Modified Wave Operators for some Hartree Type Equations II
J. Ginibre, G. Velo
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) = lam…
Scattering Theory in the Energy Space for a Class of Hartree Equations
J. Ginibre, G. Velo
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 c…
Long Range Scattering and Modified Wave Operators for some Hartree Type Equations
J. Ginibre, G. Velo
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) = lam…