## Global regularity estimates for the Boltzmann equation without cut-off

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Cyril Imbert and Luis Enrique Silvestre
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## Abstract:

We derive $C^\infty$ a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to pointwise bounds on their mass, energy and entropy densities. We also establish decay estimates for large velocities, for all derivatives of the solution.## References

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## Additional Information

**Cyril Imbert**- Affiliation: CNRS & DMA, École normale supérieure, Université PSL, CNRS, 75005 Paris, France; and 45 rue d’Ulm, 75005 Paris, France
- MR Author ID: 639611
- Email: Cyril.Imbert@ens.psl.eu
**Luis Enrique Silvestre**- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 757280
- Email: luis@math.uchicago.edu
- Received by editor(s): October 2, 2019
- Received by editor(s) in revised form: January 28, 2021, and February 12, 2021
- Published electronically: September 10, 2021
- Additional Notes: The second author was supported by NSF grant DMS-1764285
- © Copyright 2021 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**35**(2022), 625-703 - MSC (2020): Primary 35R09, 35Q20
- DOI: https://doi.org/10.1090/jams/986
- MathSciNet review: 4433077