2维定常Euler方程音速-超音速解的存在性OA
Existence of sonic-supersonic solution for two-dimensional steady Euler equations
研究广义Chaplygin气体跨音速流动问题在音速线附近的解.给定音速线和流角,构造了 2 维等熵Euler方程在音速线附近的局部解.由于该系统是退化的,在音速线上失去双曲性并产生奇点.因此通过引入一组新变量将该问题转化为一个具有显式奇异正则结构的线性系统,利用迭代法建立新系统光滑解的存在唯一性,从而证明了原系统解的存在性.
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.
肖伟;李晓蕊
长安大学 理学院,陕西 西安 710064长安大学 理学院,陕西 西安 710064
数理科学
Euler方程特征分解退化系统音速-超音速解部分速度图
Euler equationscharacteristic decompositiondegenerate systemsonic-supersonic solutionpartial hodograph
《安徽大学学报（自然科学版）》 2026 (1)
16-24,9
陕西省自然科学基础研究计划项目(2018JQ1084)
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