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June  2020, 13(3): 549-597. doi: 10.3934/krm.2020019

## Cercignani-Lampis boundary in the Boltzmann theory

 Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706, USA

Received  June 2019 Revised  December 2019 Published  March 2020

The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the local well-posedness of the Boltzmann equation in bounded domain with the Cercignani-Lampis boundary condition, which describes the intermediate reflection law between diffuse reflection and specular reflection via two accommodation coefficients. We prove the local-in-time well-posedness of the equation by establishing an $L^\infty$ estimate. In particular, for the $L^\infty$ bound we develop a new decomposition on the boundary term combining with repeated interaction through the characteristic. Moreover, under some constraints on the wall temperature and the accommodation coefficients, we construct a unique steady solution of the Boltzmann equation.

Citation: Hongxu Chen. Cercignani-Lampis boundary in the Boltzmann theory. Kinetic & Related Models, 2020, 13 (3) : 549-597. doi: 10.3934/krm.2020019
##### References:

show all references

##### References:
Maxwell boundary condition with $c = 1/2$
C-L boundary condition with $r_\perp = r_\parallel = 1/2$
C-L boundary condition with $r_\perp = r_\parallel = 1/10$
C-L boundary condition with $r_\perp = r_\parallel = 1/30$
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