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Boundary layer of the
Boltzmann equation in 2-dimensional convex domains
Lei Wu |
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Vol. 14 (2021), No. 5, 1363–1428
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Abstract |
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Consider the stationary Boltzmann equation in 2-dimensional convex domains with diffusive boundary condition. We establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier–Stokes–Fourier system with nonslip boundary conditions. Our contribution focuses on novel weighted estimates for the -Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an - framework. |
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Keywords
boundary layer, geometric correction, $W^{1,\infty}$
estimates, $L^{2m}$-$L^{\infty}$ framework
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Mathematical Subject Classification 2010
Primary: 82B40
Secondary: 34E05, 35L65
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Milestones
Received: 24 October 2018
Revised: 14 May 2019
Accepted: 27 January 2020
Published: 22 August 2021
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Authors |
| Lei Wu | |
| Department of Mathematics Lehigh University Bethlehem, PA United States |
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