Three dimensional steady subsonic Euler flows in bounded nozzles
Three dimensional steady subsonic Euler flows in bounded nozzles
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DOI：
10.1016/j.jde.2014.02.016
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发表时间：
2013-05
影响因子：
2.4
通讯作者：
Chao Chen;Chunjing Xie
中科院分区：
文献类型：
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作者：
Chao Chen;Chunjing Xie
在规定入口和出口动量的法向分量的情况下，得到了矩形喷管内亚音速三维定常欧拉流动的存在唯一性。另外，如果入口处涡度的法向分量和伯努利函数的变化量都为零，则当动量的法向分量的大小小于某一临界值时，存在唯一的亚音速势流。当动量的法向分量的大小接近临界值时，相关流动会聚为亚音速-亚音速流动。此外，当涡度的法向分量和Bernoulli函数的变化量都很小时，建立了具有非零涡度的亚音速欧拉流的存在唯一性。这些结果的证明是基于欧拉系统的新形式、具有非线性边界条件的非线性椭圆型方程的先验估计、线性div-curl系统的详细研究以及输运方程的精细估计。
The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic–sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div–curl system, and delicate estimate for the transport equations.