含引力的定常Euler方程组球对称解的适定性  

The Well-Posedness of Spherically Symmetric Solutions to the Steady Euler Equations with Gravitation

作　　者：王啟明 邓雪梅 Wang Qiming;Deng Xuemei(College of Science,China Three Gorges University,Hubei Yichang 443002;Three Gorges Mathematical Research Center,China Three Gorges University,Hubei Yichang 443002)

机构地区：[1]三峡大学理学院,湖北宜昌443002 [2]三峡大学数学研究中心,湖北宜昌443002

出　　处：《数学物理学报(A辑)》2025年第2期359-370,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(12061080)。

摘　　要：以带引力项的可压缩Euler方程组为模型,该文研究了三维球对称扩张管道中跨音速激波解的存在唯一性.假设流体受引力影响充分小,在管道入口处给定特殊的超音速初值条件,当管道出口处的压力p在某个确定范围内时,通过证明出口处压力是激波位置的严格单调函数,从而证明了管道内跨音速激波解的存在唯一性.This paper studies the existence and uniqueness of transonic shock solutions to the steady compressible Euler equations with gravity in a three-dimensional spherically symmetric divergent nozzle.Assuming that the influence of gravity on the fluid is suficiently small and the supersonic initial conditions are given at the entrance,it can be proved that when the pressure p at the exit falls in certain range,there exists a unique transonic shock solution within the nozzle by demonstrating that the pressure at the outlet is a strictly monotone function of the shock location.

关 键 词：跨音速激波解 Bernoulli函数 EULER方程组 球对称流 引力 

分 类 号：O175.2[理学—数学]