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 VlasovPoisson equation that we dubbed the VlasovDiracBenney equation or in short VDB 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.