On the Cauchy problem for Boltzmann equations: global existence and weak stability

@article{Diperna1989OnTC,
  title={On the Cauchy problem for Boltzmann equations: global existence and weak stability},
  author={Ronald J. Diperna and Pierre-Louis Lions},
  journal={Annals of Mathematics},
  year={1989},
  volume={130},
  pages={321-366}
}
We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in L' to a solution. From this stability result we deduce global existence of a solution to the Cauchy problem. Our method relies upon recent compactness results for velocity averages, a new formulation of the Boltzmann equation which involves nonlinear normalization and an analysis of… 

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