Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation


Journal Article

In this paper, we study the fluid-dynamic limit for the one-dimensional Broadwell model of the nonlinear Boltzmann equation in the presence of boundaries. We consider an analogue of Maxwell's diffusive and reflective boundary conditions. The boundary layers can be classified as either compressive or expansive in terms of the associated characteristic fields. We show that both expansive and compressive boundary layers (before detachment) are nonlinearly stable and that the layer effects are localized so that the fluid dynamic approximation is valid away from the boundary. We also show that the same conclusion holds for short time without the structural conditions on the boundary layers. A rigorous estimate for the distance between the kinetic solution and the fluid-dynamic solution in terms of the mean-free path in the L∞ -norm is obtained provided that the interior fluid flow is smooth. The rate of convergence is optimal.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Xin, Z

Published Date

  • October 18, 1996

Published In

Volume / Issue

  • 135 / 1

Start / End Page

  • 61 - 105

International Standard Serial Number (ISSN)

  • 0003-9527

Digital Object Identifier (DOI)

  • 10.1007/BF02198435

Citation Source

  • Scopus