Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary

Hongxu Chen; Chanwoo Kim

doi:10.3934/krm.2024001

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2024, Volume 17, Issue 5: 774-806. Doi: 10.3934/krm.2024001 Free Access

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Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary

Hongxu Chen^1, , and
Chanwoo Kim^2,

1.
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
2.
Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA

^*Corresponding author: Hongxu Chen
^*Corresponding author: Hongxu Chen

Received: July 2023

Revised: January 2024

Early access: January 18, 2024

Published online: January 18, 2024

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Abstract

In this short note, we prove an $ L^6 $-control of the macroscopic part of the linear Boltzmann and Landau equations. This result is an extension of the test function method of Esposito-Guo-Kim-Marra [4][5] to the specular reflection boundary condition, in which we crucially used the Korn's inequality [3] and the system of symmetric Poisson equations [2].

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Mathematics Subject Classification: Primary: 35Q20, 82C40; Secondary: 35B40.

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References

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