This is part of my lecture notes on Kinetic Theory of Gases, taught at Penn State last semester, Fall 2017. In this part, I’d like to introduce this nice BardosDegond 1985’s global solutions to the VlasovPoisson system. Of course, the global smooth solutions are already constructed, without any restriction on size of initial data (e.g., Pfaffelmoser, Schaeffer ’91; see also the previous lecture), however they give no information on their asymptotic behavior at large time. Now, for initial data that are sufficiently small near zero, Bardos and Degond were able to construct global smooth solutions that decay in large time. To my knowledge, this was the first result where dispersion is rigorously shown for kinetic equations (they appear to be motivated by similar results for nonlinear wave equations where dispersion was (still is) the key to deduce the global behavior at the large time; e.g., Klainerman, Ponce, Shatah, among others, in the early 80s).
Posts Tagged ‘Dispersive estimates’
BardosDegond’s solutions to VlasovPoisson
Posted in Kinetic theory, Math 597C: Graduate topics course on Kinetic Theory, tagged BardosDegond, Dispersive estimates, VlasovPoisson on March 1, 2018 Leave a Comment »
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