EXISTENCE OF BOUNDARY LAYER SOLUTIONS TO THE BOLTZMANN EQUATION-Reference-Cited by-同舟云学术

EXISTENCE OF BOUNDARY LAYER SOLUTIONS TO THE BOLTZMANN EQUATION

Published:2004-10 Issue:04 Volume:02 Page:337-363
ISSN:0219-5305
Container-title:Analysis and Applications
language:en
Short-container-title:Anal. Appl.

Author:

CHEN CHIUN-CHUAN¹,LIU TAI-PING²,YANG TONG³

Affiliation:

1. Department of Mathematics, National Taiwan University, Taipei, Taiwan, R.O.C

2. Department of Mathematics, Stanford University, Stanford, CA 94305, USA

3. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China

Abstract

In this paper, we consider the existence of boundary layer solutions to the Boltzmann equation for a hard potential with angular cut-off. The boundary condition is imposed for incoming particles of Dirichlet type and the solution tends to a global Maxwellian in the far field. Similar to the problem on the hard sphere model studied in [17], the existence of a solution is shown to depend on the Mach number of the far field Maxwellian, and there is an implicit solvability conditions yielding the co-dimensions of the boundary data. For hard potential models, the shape of the boundary layers is richer. This compels the introduction of a new norm which is a function of both position and velocity.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219530504000400

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