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The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in Fluid Mechanics and Semi-classical Limits

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If you have a question about this talk, please contact Prof. Clément Mouhot.

This contribution concerns a one-dimensional version of the Vlasov equation dubbed the Vlasov−Dirac−Benney equation (in short V−D−B) where the self interacting potential is replaced by a Dirac mass. Emphasis is put on the relations between the linearized version, the full nonlinear problem and equations of fluids. In particular the connection with the so called Benney equation leads to new stability results. Eventually the V−D−B appears to be at the “cross road” of several problems of mathematical physics which have as far as stability is concerned very similar properties. This is a joint work Nicolas Besse.

This talk is part of the Partial Differential Equations seminar series.

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