The Green's function for the 3D modified Vlasov-Poisson-Boltzmann system decomposes into diffusive waves, Huygens waves with speed sqrt(8/3), a singular kinetic wave, and an exponentially decaying term, supporting pointwise estimates for the nonlinear global solution.
Deng, Global regularity of the Vlasov-Poisson-Boltzmann system near Maxwellian without angular cutoff for soft potential
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Green's Function and Pointwise Space-time Behaviors of the three-Dimensional modified Vlasov-Poisson-Boltzmann System
The Green's function for the 3D modified Vlasov-Poisson-Boltzmann system decomposes into diffusive waves, Huygens waves with speed sqrt(8/3), a singular kinetic wave, and an exponentially decaying term, supporting pointwise estimates for the nonlinear global solution.