Kinetic-fluid boundary layers and acoustic limit for the Boltzmann equation with general Maxwell reflection boundary condition
Year: 2024
Type: article
Abstract: We prove the acoustic limit from the Boltzmann equation with hard sphere collisions and the Maxwell reflection boundary condition. Our construction of solutions includes the interior fluid part and Knudsen-viscous coupled boundary layers. The main novelty is that the accommodation coefficient is in the full range $ 0<\alpha\leq 1 $. The previous works in the context of classical solutions only considered the simplest specular reflection boundary condition, i.e., $ \alpha = 0 $. The mechanism of the derivation of fluid boundary conditions in the case $ \alpha = O(1) $ is quite different from the cases $ \alpha = 0 $ or $ \alpha = o(1) $. This rigorously justifies the corresponding formal analysis in Sone's books [33,34]. In particular, this is a smooth solution analogue of [24], in which the renormalized solution was considered and the boundary layers were not visible.
Source: Kinetic and Related Models
DOI: 10.3934/krm.2024029
Authors: Ning Jiang, Yulong Wu
Institution: Wuhan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405599276