The cauchy problem for the vlasov-dirac-benney equation and related issues in fluid mechanics and semi-classical limits

Abstract

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 © American Institute of Mathematical Sciences.