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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Global regularity estimates for the Boltzmann equation without cut-off
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by Cyril Imbert and Luis Enrique Silvestre HTML | PDF
J. Amer. Math. Soc. 35 (2022), 625-703 Request permission


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.
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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:
  • Luis Enrique Silvestre
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • MR Author ID: 757280
  • Email:
  • 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:
  • MathSciNet review: 4433077