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On the Fokker-Planck-Boltzmann equation. (English) Zbl 0671.35068
Summary: We consider the Boltzmann equation perturbed by Fokker-Planck type operator. To overcome the lack of strong a priori estimates and to define a meaningful collision operator, we introduce a notion of renormalized solution which enables us to establish stability results for sequences of solutions and global existence for the Cauchy problem with large data. The proof of stability and existence combines renormalization with an analysis of a defect measure.

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35B20 Perturbations in context of PDEs
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35G25 Initial value problems for nonlinear higher-order PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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