安徽大学学报（自然科学版）2026，Vol.50Issue(1)：16-24,9.DOI:10.3969/j.issn.1000-2162.2026.01.003
2维定常Euler方程音速-超音速解的存在性
Existence of sonic-supersonic solution for two-dimensional steady Euler equations
摘要
Abstract
We studied the sonic-supersonic solution near the sonic curve for the generalized Chaplygin gas.Given the sonic curve and the flow angle,a local solution of the two-dimensional isentropic Euler equation near the sonic curve was constructed.Since the system was degenerate,it lost hyperbolicity on the sonic curve and developed singularities.Therefore,the problem was transformed into a linear system with an explicit singular regular structure by introducing a new set of variables.We established the existence and uniqueness of smooth solutions for the new system by an iterative method and proved the existence of solutions for the original system.关键词
Euler方程/特征分解/退化系统/音速-超音速解/部分速度图Key words
Euler equations/characteristic decomposition/degenerate system/sonic-supersonic solution/partial hodograph分类
数理科学引用本文复制引用
肖伟,李晓蕊..2维定常Euler方程音速-超音速解的存在性[J].安徽大学学报（自然科学版）,2026,50(1):16-24,9.基金项目
陕西省自然科学基础研究计划项目(2018JQ1084) （2018JQ1084）
