论文标题
在轴对称相对论跨多声流中产生的超音速斑块的溶液的存在和规律性，状态的一般方程
Existence and regularity of solutions of a supersonic-sonic patch arising in axisymmetric relativistic transonic flow with general equation of state
论文作者
论文摘要
在本文中，我们证明了在修改后的Frankl问题中出现的平滑溶液的存在和规律性，在对三维轴对称稳定稳定稳定相对论的跨性别跨性别流在对称翼型上的研究中。我们考虑了一个一般的状态凸方程，这使得这个问题在跨音量流的一般理论的背景下变得复杂且有趣。这种类型的斑块出现在许多跨音量流中，在机翼和喷嘴喉咙附近的流动中出现。这里的主要困难是由于轴对称性和相对论流的声音堕落而导致非均匀项的耦合。但是，使用角度变量的良好特征分解和部分Hodograph Transformation，我们首先证明了部分hodograph平面中溶液的存在和规律性。此外，通过使用反变形，我们在物理平面中构造平滑的解决方案，并讨论溶液的均匀规则性，直到相关的声音曲线。最后，我们还讨论了声音曲线的均匀规律性。
In this article, we prove the existence and regularity of a smooth solution for a supersonic-sonic patch arising in a modified Frankl problem in the study of three-dimensional axisymmetric steady isentropic relativistic transonic flows over a symmetric airfoil. We consider a general convex equation of state which makes this problem complicated as well as interesting in the context of the general theory for transonic flows. Such type of patches appear in many transonic flows over an airfoil and flow near the nozzle throat. Here the main difficulty is the coupling of nonhomogeneous terms due to axisymmetry and the sonic degeneracy for the relativistic flow. However, using the well-received characteristic decompositions of angle variables and a partial hodograph transformation we prove the existence and regularity of solution in the partial hodograph plane first. Further, by using an inverse transformation we construct a smooth solution in the physical plane and discuss the uniform regularity of solution up to the associated sonic curve. Finally, we also discuss the uniform regularity of the sonic curve.
