$L^2$ Diffusive Expansion For Neutron Transport Equation

Yan Guo; Lei Wu

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arXiv · 2301.11996

$L^2$ Diffusive Expansion For Neutron Transport Equation

Yan Guo·Lei Wu

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Abstract

Grazing set singularity leads to a surprising counter-example and breakdown of the classical mathematical theory for $L^{\infty}$ diffusive expansion of neutron transport equation with in-flow boundary condition in term of the Knudsen number $\varepsilon$, one of the most classical problems in the kinetic theory. Even though a satisfactory new theory has been established by constructing new boundary layers with favorable $\varepsilon$-geometric correction for convex domains, the severe grazing singularity from non-convex domains has prevented any positive mathematical progress. We develop a novel and optimal $L^2$ expansion theory for general domain (including non-convex domain) by discovering a surprising $\varepsilon^{\frac{1}{2}}$ gain for the average of remainder.

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Yan Guo, Lei Wu. 2023-01-27. $L^2$ Diffusive Expansion For Neutron Transport Equation. https://arxiv.org/abs/2301.11996

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