Hydrodynamic limit with geometric correction of stationary Boltzmann equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Wu, Lei¹ 

[1] Carnegie Mellon Univ, Dept Math Sci, Wean Hall 6113, Pittsburgh, PA 15213 USA

关键词: Normal singularity;    Boundary layer;    Geometric correction;    Boussinesq relation;   

DOI  :  10.1016/j.jde.2016.01.024

来源: Elsevier

【 摘 要 】

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in L-infinity both for its proof and result. Also, we show the hydrodynamic limit with a different boundary layer expansion with geometric correction. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free