Boltzmann Equation with Cercignani-Lampis Boundary Condition in Bounded Domain
Time: 2019-06-18
Published By: Xiaoni Tan
Speaker(s): Hongxu Chen (University of Wisconsin-Madison)
Time: 16:00-17:00 June 24, 2019
Venue: Room 78201, Jingchunyuan 78, BICMR
When dilute gas is confined in a bounded domain, boundary effects play an important role. [1] established the classical solution for the Boltzmann equation with various boundary condition: diffuse, specular reflection and bounce back. The Cercignani-Lampis(C-L) boundary condition, derived in [2], is a model for gas-surface interaction that encompass the pure diffusion and pure reflection via two accommodation coefficients. The complexity of the scattering kernel in the boundary condition brings the difficulty in the analysis. In this talk I will present the local well-posedness of the Boltzmann equation with the C-L boundary condition. In particular, I will focus on the L^\infty estimate. Then I will present an extension work on the local well-posedness of the Vlasov-Possion-Boltzmann equation with the same boundary condition, which describes the charged dilute gas with self-imposed electric fields.