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In this short note, we prove an $L^6$-control of the macroscopic part of thelinear Boltzmann and Landau equations. This result is an extension of the testfunction method of Esposito-Guo-Kim-Marra~\cite{EGKM}\cite{EGKM2} to thespecular reflection boundary condition, in which we crucially used the Korn'sinequality \cite{DV2} and the system of symmetric Poisson equations\cite{Bernou}.

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