On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: Global existence of weak solutions |
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Authors: | Xuguang Lu |
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Institution: | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China |
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Abstract: | 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<γ?−3) with a weak angular cutoff. In particular the Coulomb interaction (γ=−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. |
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Keywords: | Boltzmann equation Fermi-Dirac particles Coulomb interaction Weak angular cutoff Global existence |
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