The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Kinetic and Related Models Year : 2013

The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits

Claude Bardos
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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.

Dates and versions

hal-00925109 , version 1 (07-01-2014)

Identifiers

Cite

Claude Bardos, Nicolas Besse. The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits. Kinetic and Related Models , 2013, 6, pp.893-917. ⟨10.3934/krm.2013.6.893⟩. ⟨hal-00925109⟩
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