Uniqueness and Instability of Subsonic--Sonic Potential Flow in A Convergent Approximate Nozzle
Uniqueness and Instability of Subsonic--Sonic Potential Flow in A Convergent Approximate Nozzle
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DOI：
10.1090/s0002-9939-10-10202-0
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发表时间：
2009-09
期刊：
影响因子：
--
通讯作者：
Pan Liu;Hairong Yuan
中科院分区：
文献类型：
--
作者：
Pan Liu;Hairong Yuan
在具有收敛截面的曲面上，证明了可压缩势流方程对称亚声速-声速流动解的唯一性和不稳定性。在空气动力学中，这种表面可以看作是二维收敛喷管的近似。在数学上，这是一类具有伯努利型边界条件的非线性退化椭圆方程的唯一性和不存在性结果。该证明依赖于极大值原理和本文所证明的一个广义Hopf边点引理。
We proved uniqueness and instability of the symmetric subsonic--sonic flow solution of the compressible potential flow equation in a surface with convergent areas of cross--sections. Such a surface may be regarded as an approximation of a two--dimensional convergent nozzle in aerodynamics. Mathematically these are uniqueness and nonexistence results of a nonlinear degenerate elliptic equation with Bernoulli type boundary conditions. The proof depends on maximum principles and a generalized Hopf boundary point lemma which was proved in the paper.