On the Fokker-Planck-Boltzmann equation

DiPerna, R.J.; Lions, Pierre-Louis

DiPerna, R.J.; Lions, Pierre-Louis (1988), On the Fokker-Planck-Boltzmann equation, Communications in Mathematical Physics, 120, 1, p. 1-23. http://dx.doi.org/10.1007/BF01223204

Type

Article accepté pour publication ou publié

Date

1988

Journal name

Communications in Mathematical Physics

Volume

120

Number

Publisher

Springer

Pages

1-23

Abstract (EN)

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.

Subjects / Keywords

Fokker-Planck type operator; Boltzmann equation