On the Cauchy Problem for the Fokker-Planck-Boltzmann Equation With Infinite Initial Energy
DOI:
https://doi.org/10.5644/SJM.05.1.06Keywords:
Fokker-Planck-Boltzmann equation, renormalized solution, dispersive effectsAbstract
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 $f_0(|x|^\alpha+|x-v|^2)\in L^1$ instead of $f_0(|x|^2+|v|^2)\in L^1$.
2000 Mathematics Subject Classification. 35Q35, 76P05, 82C40
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