Semi-classical Limit of an Infinite Dimensional System of Nonlinear Schrödinger Equations
by Claude Bardos   Nicolas Besse  

Vol. 11 No. 1 (2016) P.43~P.61

ABSTRACT

We study the semi-classical limit of an infinite dimensional system of coupled nonlinear Schrödinger equations towards exact weak solutions of the Vlasov-Dirac-Benney equation, for initial data with analytical regularity in space. After specifying the right analytic extension of the problem and solutions, the proof relies on a suitable version of the Cauchy-Kowalewski Theorem and energy estimates in Hardy type spaces with convenient analytic norms. This contribution presents a detailed and probably optimal (with complete proofs) version of results announced in the more general setting in [1] and [2].

KEYWORDS
Vlasov equation with Dirac potential, Vlasov-Dirac-Benney equation, Nonlinear Schrödinger equations, semi-classical limits.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary: 3Q83, 75X05; Secondary: 82D10.

MILESTONES

Received: 2015-05-06
Revised : 2015-06-29
Accepted: 2015-06-30

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