On the Cauchy Problem for the Fokker-Planck-Boltzmann Equation With Infinite Initial Energy - Zheng, Minling; Chu, Yuming (Sarajevo Journal of Mathematics, 2024)
We prove a new existence result for the Fokker-Planck-Boltzmann equation with an initial data with infinite energy in the framework of renormalization. We extend the result of DiPerna-Lions by assuming $f_0(|x|^α+|x-v|^2)\in L^1$ instead of $f_0(|x|^2+|v|^2)\in L^1$. 2000 Mathematics Subject Classification. 35Q35, 76P05, 82C40