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Commutator method for
averaging lemmas
Pierre-Emmanuel Jabin, Hsin-Yi Lin and Eitan Tadmor |
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Vol. 15 (2022), No. 6, 1561–1584
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Abstract |
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We introduce a commutator method with multiplier to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. Our method requires only elementary techniques in Fourier analysis and highlights a new range of assumptions that are sufficient for the velocity average to be in . Our result provides a direct proof (without interpolation) and improves the regularizing result for the measure-valued solutions to scalar conservation laws in space dimension 1. |
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Keywords
velocity-averaging lemma, kinetic transport equation,
dispersion, singular integral, multiplier, scalar
conservation law, measure-valued solution
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Mathematical Subject Classification
Primary: 35B65
Secondary: 35L65, 35Q83, 42B37
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Milestones
Received: 12 May 2020
Revised: 12 November 2020
Accepted: 16 February 2021
Published: 10 November 2022
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Authors |
| Pierre-Emmanuel Jabin | |
| Department of Mathematics and Huck
Institutes of the Life Sciences Pennsylvania State University State College, PA United States |
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| Hsin-Yi Lin | |
| CIRES University of Colorado Boulder, CO United States |
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| Eitan Tadmor | |
| Department of Mathematics and
Institute for Physical Sciences and Technology University of Maryland College Park, MD United States |
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