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On the Fokker-Planck-Boltzmann equation

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
1
Publisher
Springer
Pages
1-23
Publication identifier
http://dx.doi.org/10.1007/BF01223204
Metadata
Show full item record
Author(s)
DiPerna, R.J.
Lions, Pierre-Louis
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

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