American Institute of Mathematical Sciences

October  2019, 12(5): 1163-1183. doi: 10.3934/krm.2019044

Uniform estimates on the Fisher information for solutions to Boltzmann and Landau equations

 1 Departamento de Matemática, PUC-Rio, Rua Marquês de São Vicente 225, Rio de Janeiro, CEP 22451-900, Brazil 2 Université Clermont Auvergne, LMBP, UMR 6620 - CNRS, Campus des Cézeaux, 3, place Vasarely, TSA 60026, CS 60026, F-63178 Aubière Cedex, France 3 Università degli Studi di Torino & Collegio Carlo Alberto, Department ESOMAS, Corso Unione Sovietica, 218/bis, 10134 Torino, Italy

* Corresponding author

Received  February 2019 Revised  April 2019 Published  July 2019

Fund Project: B. L gratefully acknowledges the financial support from the Italian Ministry of Education, University and Research (MIUR), "Dipartimenti di Eccellenza" grant 2018-2022.

In this note we prove that, under some minimal regularity assumptions on the initial datum, solutions to the spatially homogenous Boltzmann and Landau equations for hard potentials uniformly propagate the Fisher information. The proof of such a result is based upon some explicit pointwise lower bound on solutions to Boltzmann equation and strong diffusion properties for the Landau equation. We include an application of this result related to emergence and propagation of exponential tails for the solution's gradient. These results complement estimates provided in [24,26,15,23].

Citation: Ricardo J. Alonso, Véronique Bagland, Bertrand Lods. Uniform estimates on the Fisher information for solutions to Boltzmann and Landau equations. Kinetic & Related Models, 2019, 12 (5) : 1163-1183. doi: 10.3934/krm.2019044
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