Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 245, Issue 7, Pages 1705-1761Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2008.06.028
Keywords
Boltzmann equation; Fermi-Dirac particles; Coulomb interaction; weak angular cutoff; global existence
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Funding
- National Natural Science Foundation of China [10571101]
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For general initial data we prove the global existence and weak stability of weak solutions of the Boltzmann equation for Fermi-Dirac particles in a periodic box for very soft potentials (-5 < gamma <= -3) with a weak angular cutoff. In particular the Coulomb interaction (gamma = -3) with the weak angular cutoff is included. The conservation of energy and moment estimates are also proven under a further angular cutoff. The proof is based on the entropy inequality, velocity averaging compactness of weak solutions, and various continuity properties of general Boltzmann collision integral operators. (C) 2008 Elsevier Inc. All rights reserved.
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