Abstract
The aim of this paper is to show that moment approximations of kineticequations based on a maximum-entropy approach can suffer from severedrawbacks if the kinetic velocity space is unbounded. As example, westudy the Fokker-Planck equation where explicit expressions for themoments of solutions to Riemann problems can be derived. The quality ofthe closure relation obtained from the maximum-entropy approach as wellas the Hermite/Grad approach is studied in the case of five moments. Itturns out that the maximum-entropy closure is even singular inequilibrium states while the Hermite/Grad closure behaves reasonably. Inparticular, the admissible moments may lead to arbitrarily large speeds ofpropagation, even for initial data arbitrary close to global eqilibrium.
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