Gaussian Lower Bounds for the Boltzmann Equation without Cutoff

@article{Imbert2020GaussianLB,
  title={Gaussian Lower Bounds for the Boltzmann Equation without Cutoff},
  author={Cyrille Imbert and Cl{\'e}ment Mouhot and Luis Silvestre},
  journal={SIAM J. Math. Anal.},
  year={2020},
  volume={52},
  pages={2930-2944}
}
The study of positivity of solutions to the Boltzmann equation goes back to Carleman (1933), and the initial argument of Carleman was developed byPulvirenti-Wennberg (1997), the second author and Briant (2015). The appearance of a lower bound with Gaussian decay had however remained an open question for long-range interactions (the so-called non-cutoff collision kernels). We answer this question and establish such Gaussian lower bound for solutions to the Boltzmann equation without cutoff, in… 

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