Section: New Results

Semi-classical limit of an infinite dimensional system of nonlinear Schrödinger equations

Participants : Claude Bardos, Nicolas Besse [correspondent] .

In this paper [24] , 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.