论文标题
在稳定电势流中，附着的跨音速冲击的稳定性超过三维楔子
Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges
论文作者
论文摘要
我们开发了一种新的方法，并利用它来建立附着的弱跨性别冲击的全球存在和非线性结构稳定性，这是在三维楔形的稳定电势流中；特别是，删除了前面结果中扰动远离楔形边缘的限制。关键要素之一是基于边界条件的非杂交性，确定沿楔形边界边界条件的边界操作员的“良好”方向。通过识别该方向，可以分配楔形边缘上的附加边界条件，以确保冲击在边缘附加并在小扰动下线性稳定。基于线性稳定性，我们引入了迭代方案，并证明存在迭代方案的独特固定点，这导致了附着的弱透射冲击的全局存在和非线性结构稳定性。这种方法既不基于霍德仪的变换也不基于频谱分析，并且对于其他类似困难的问题应该有用。
We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the perturbation is away from the wedge edge in the previous results is removed. One of the key ingredients is to identify a "good" direction of the boundary operator of a boundary condition of the shock along the wedge edge, based on the non-obliqueness of the boundary condition for the weak shock on the edge. With the identification of this direction, an additional boundary condition on the wedge edge can be assigned to make sure that the shock is attached on the edge and linearly stable under small perturbation. Based on the linear stability, we introduce an iteration scheme and prove that there exists a unique fixed point of the iteration scheme, which leads to the global existence and nonlinear structural stability of the attached weak transonic shock. This approach is based on neither the hodograph transformation nor the spectrum analysis, and should be useful for other problems with similar difficulties.
