Section: New Results

Hamiltonian structure, fluid representation, stability for the Vlasov-Dirac-Benney equation

Participants : Claude Bardos, Nicolas Besse [correspondent] .

This contribution [23] is an element of a research program devoted to the analysis of a variant of the Vlasov$-$Poisson equation that we dubbed the Vlasov$-$Dirac$-$Benney equation or in short V$-$D$-$B equation. As such it contains both new results and efforts to synthesize previous observations. One of main links between the different issues is the use of the energy of the system. In some cases, such energy becomes a convex functional and allows to extend to the present problem the methods used in the study of conservation laws. Such use of the energy is closely related to the Hamiltonian structure of the problem.