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Global Solutions to the L{sup 2}--Critical Schroedinger--Poisson System

Journal Article · · AIP Conference Proceedings
DOI:https://doi.org/10.1063/1.3030805· OSTI ID:21251629
;  [1]
  1. Faculty of Applied Mathematics and Informatics, Technical University of Sofia 1000 Sofia (Bulgaria)
The main purpose of the present paper is to study the global behavior of solutions to the L{sup 2}-critical Schroedinger-Poisson system i{partial_derivative}{sub t}{psi}(t,x)+{delta}{psi}(t,x) = V(t,x){psi}(t,x), (t,x)(set-membership sign)R{sub +}xR{sup 3}, {delta}V(t,x) = -4{pi}|{psi}(t,x)|{sup (8/3)}, {psi}(0,x) = {psi}{sub 0}(x). More precisely, we shall establish the local existence of solutions for initial data {psi}{sub 0} in L{sup 2}(R{sup 3}), as well as the existence of global solutions for small initial data. Finally, we shall prove the existence of scattering operator.
OSTI ID:
21251629
Journal Information:
AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1067; ISSN APCPCS; ISSN 0094-243X
Country of Publication:
United States
Language:
English

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