STABILITY OF CYLINDRICAL TRANSONIC SHOCKS FOR THE TWO-DIMENSIONAL STEADY COMPRESSIBLE EULER SYSTEM
STABILITY OF CYLINDRICAL TRANSONIC SHOCKS FOR THE TWO-DIMENSIONAL STEADY COMPRESSIBLE EULER SYSTEM
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DOI：
10.1142/s0219891608001519
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发表时间：
2008-06
影响因子：
0.7
通讯作者：
Li Liu;Hairong Yuan
中科院分区：
文献类型：
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作者：
Li Liu;Hairong Yuan
建立了二维完全可压缩定常Euler方程组的一类圆柱对称跨音速激波的稳定性。这一结果部分解释了空气动力学中常用的准一维喷管流动模型的有效性。在数学上，我们求解了一个椭圆-双曲组合方程组的非线性自由边界问题，该方程组以圆形跨音速激波阵面为自由边界。我们通过找到一个适当定义的边界轮廓更新映射的（局部）唯一不动点来实现这一点。为了定义这个映射，我们遇到了一系列的非经典边界值问题的环，这涉及到一种新的类型的非局部椭圆问题，和积分样的可解性条件，以确定自由边界的位置。这反映了椭圆-双曲组合方程组边值问题的一个有趣的新特征。
We establish the stability of a class of cylindrical symmetric transonic shocks for two-dimensional complete compressible steady Euler system. This result partly explains the effectiveness of the popular quasi-one-dimensional model of nozzle flows used in aerodynamics. Mathematically, we solve a nonlinear free boundary problem of an elliptic-hyperbolic composite system, with the circular transonic shock front as the free boundary. We accomplish this by finding a (locally) unique fixed point of an appropriately defined boundary profile updating mapping. To define this mapping, we encounter a series of nonclassical boundary value problems in an annulus, which involve a new type of nonlocal elliptic problem, and integral-like solvability conditions to determine the position of the free boundary. This reflects an interesting new feature of boundary value problems of elliptic-hyperbolic composite systems.