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Stability of equilibria for a Hartree equation for random fields
Journal de Mathématiques Pures et Appliquées ( IF 1.961 ) Pub Date : 2020-03-23 , DOI: 10.1016/j.matpur.2020.03.003
C. Collot; A.-S. de Suzzoni

We consider a Hartree equation for a random field, which describes the temporal evolution of infinitely many fermions. On the Euclidean space, this equation possesses equilibria which are not localized. We show their stability through a scattering result, with respect to localized perturbations in the not too focusing case in high dimensions d≥4. This provides an analogue of the results of Lewin and Sabin [22], and of Chen, Hong and Pavlović [11] for the Hartree equation on operators. The proof relies on dispersive techniques used for the study of scattering for the nonlinear Schrödinger and Gross-Pitaevskii equations.
更新日期:2020-03-24

 

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