球坐标系下Chaplygin气体中3维定常位势流方程的比较原理  

Comparison Principles for 3-D Steady Potential Flow of Chaplygin Gas in Spherical Coordinates

作　　者：龙柄菘 Bing Song LONG(School of Mathematics and Statistics,Huanggang Normal University,Hubei 438000,P.R.China)

机构地区：[1]黄冈师范学院数学与统计学院,湖北438000

出　　处：《数学学报（中文版）》2024年第6期1198-1206,共9页Acta Mathematica Sinica：Chinese Series

基　　金：湖北省自然科学基金青年项目(2024AFB007);黄冈师范学院博士科研项目(204202302)。

摘　　要：本文研究了Chaplygin气体中三维定常可压缩位势流方程.在球坐标系下,位势流方程可在单位球面上转化为一个混合型方程.以三角翼超音速绕流问题为背景,本文针对此方程带有一类混合边值条件的情形建立了比较原理,并在此基础上构造了问题解的一个L^(∞)先验估计.这个估计是说明方程在抛物-椭圆区域内为椭圆型的关键.In this paper,we consider the 3-D steady compressible potential flow of Chaplygin gas.In spherical coordinates,the potential equation is of mixed type in the unit sphere.For the problem of supersonic flow over a delta wing,we establish a comparison principle for elliptic solutions of the equation with a class of mixed boundary conditions.We employ this comparison principle to derive an L^(∞) estimate,which is the key to show that the equation is elliptic in the parabolic-elliptic region.

关 键 词：Chaplygin气体 三维定常位势流方程 混合型方程 比较原理 

分 类 号：O175[理学—数学]