Methods and Applications of Analysis

Volume 14 (2007)

Number 4

Pointwise convergence of the boundary layer of the Boltzmann equation for the cutoff hard potential

Pages: 307 – 344

DOI: http://dx.doi.org/10.4310/MAA.2007.v14.n4.a2

Authors

Shijin Deng

Weike Wang

Shih-Hsien Yu

Abstract

In this paper, we consider the nonlinear stability of a boundary layer of the Boltzmann equation with the cutoff hard potential when Mach number at far-field is greater than 1. Based on the Green's function for the Cauchy problem constructed in M.-Y. Lee, T.-P. Liu and S.-H. Yu and the weighted energy method, we obtain the estimates for the Green's function of the initial boundary problem and use it to obtain the nonlinear stability with an almost exponential convergent rate to the nonlinear Knudsen layer.

Keywords

Boltzmann equation; cutoff hard potential; boundary layer; the Green's function; pointwise estimate

2010 Mathematics Subject Classification

82C40

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