L2 Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects-Reference-Cited by-同舟云学术

L2 Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects

Published:1997-12 Issue:08 Volume:07 Page:1051-1083
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Castella F.¹

Affiliation:

1. Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, BC 187, Tour 55-65, 5ème étage, 4 place Jussieu, 75252 Paris Cedex 5, France

Abstract

We study a system of infinitely many coupled Schrödinger equations with self-consistent Coulomb potential as the initial data has only a regularity of L2-type. We first establish Strichartz' inequalities in the framework of vector-valued wave functions (density matrices). This allows us to prove a well-posedness result, and strong smoothing effects. Also, we state blow-up (resp. decay) estimates for the solution as time goes to zero (resp. infinity).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202597000530

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