2016 / March Volume 11 No.1
Semi-classical Limit of an Infinite Dimensional System of Nonlinear Schrödinger Equations
| Published Date |
2016 / March
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| Title | Semi-classical Limit of an Infinite Dimensional System of Nonlinear Schrödinger Equations |
| Author | |
| Keyword | |
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| Pagination | 43-61 |
| 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].
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| AMS Subject Classification |
Primary: 3Q83, 75X05; Secondary: 82D10.
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| Received |
2015-06-29
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| Accepted |
2015-06-30
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