轴对称可压缩空腔流问题轴向速度的正性  

Positivity of the axial velocity for axially symmetric compressible cavity flow problem

作　　者：王欣 WANG Xin(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报(自然科学版)》2025年第2期328-333,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省青年科技创新研究团队项目(2021JDTD0024);重庆市教委科学技术研究项目(KJQN202403428)。

摘　　要：空腔流包含旋涡运动、剪切层干扰等复杂物理现象.高速空腔流可能导致飞行器内部空腔中的设备产生疲劳或损坏.空腔流理论是流体力学研究的一个热点,能够为飞行器的设计和性能提升提供理论基础.Alt-Caffarelli-Friedman关于三维轴对称可压缩空腔流问题的研究建立了流体亚音速解的适定性结果,以及可压缩亚音速空腔流自由边界的凸性.本文基于自由边界的凸几何性质证明了流体轴向速度的正性.进一步,在自由边界严格凸的条件下,本文得到了自由边界在分离点处的最优正则性.Cavity flows contain complex physical phenomena such as vortex motion and shear layer interference.High-speed cavity flows may cause fatigue damage to the components and equipment in the cavity of an aircraft easily.Therefore,cavity flow theory plays an important role in improving aircraft performance while it has always been a research hotspot in fluid mechanics.In the work on the 3D axially symmetric compressible cavity flow by Alt-Caffarelli-Friedman,the well-posedness result on the subsonic solution was established.As byproducts,they also obtained the convexity of the free boundary for the compressible subsonic cavity flow.In this paper,based on the convex geometry property of the free boundary,the positivity of the axial velocity in the fluid is proved.Furthermore,under the strictly convex condition of the free boundary,the optimal regularity of the free boundary at the separation point is also obtained.

关 键 词：可压缩空腔流 轴向速度 自由边界 最优正则性 

分 类 号：O29[理学—应用数学]