Regularity and propagation of moments in some nonlinear Vlasov systems

By I. Gasser, Pierre-Emmanuel Jabin, Benoit Perthame. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000

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Moment Propagation for Weak Solutions to the Vlasov–Poisson System (2012, background): “The propagation property (5) was obtained in references [5] whenever k > 3 and [2] when k ∈ 2 3 at the expense of an additional space-moment assumption.”
Mathematical tools for kinetic equations (2004, methodology): “For instance the Vlasov-Stokes system reads [80], [56]: ∂ ∂t f + ξ · ∇xf + divξ[(U − ξ)f ] = 0, t ≥ 0, x, ξ ∈ R, (40)”
A review of the mean field limits for Vlasov equations (2014, background): “Global strong solutions were finally obtained in [137], [143] (see also [95]) and at the same time in [119], see [68] and [71] as well.”
Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory (2002, background): “Apart from the study of the Boltzmann equation, renormalization and velocityaveraging lemmas have become popular tools for the study of various kinetic equations [191, 375, 318, 176, 229], ordinary differential equations with nonsmooth (Sobolev-regular) coefficients [193, 97], or the reformulation o”