Free molecular flow with boundary effect
type: Item
instance of: scholarly article
title: Free molecular flow with boundary effect
zbMATH Open document ID: 1263.82043
author: Hung-Wen Kuo
author: Tai-Ping Liu
author: Li-Cheng Tsai
published in: Communications in Mathematical Physics
publication date: 2013-03-18T00:00:00Z
review text: The purpose of this paper is to focus on the dissipative effect of the boundary condition and establish the convergence rate to equilibrium of free molecular gas flow in spatial dimensions \(d.\) The authors consider the free molecular equation: \[ \frac{\partial{\bar{f}}}{\partial t}+\sum_{i=1}^d\zeta_i\frac{\partial{\bar{f}}}{\partial x_i} =0,\;\;\; \bar{f}=\bar{f}(\mathbf{x},\zeta,t), \] \[ \bar{f}(\mathbf{x},\zeta,0)=\bar{f_{in}}(\mathbf{x},\zeta)\text{ given, } \mathbf{x}\in D\subset\mathbb R^d,\zeta\in\mathbb R^3, t\in\mathbb R_{+}, \] where \(\mathbf{x}\) is the spatial coordinate, \(\zeta\) is the microscopic velocity, \(t\) is the temporal coordinate, and \(\bar{f}=\bar{f_{in}}(\mathbf{x},\zeta)\) is the density function in \((\mathbf{x},\zeta)\) of a gas molecule at time \(t.\) The authors obtain the optimal convergence rates of \((t+1)^{-d}\).
reviewed by: Dazmir Shulaia
Mathematics Subject Classification ID: 82C40
zbMATH DE Number: 6145995
MaRDI profile type: Publication
full work available at URL: s00220-013-1662-9
OpenAlex ID: W2036099173
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DOI: 10.1007/S00220-013-1662-9
description: scientific article; zbMATH DE number 6145995