一个时间周期分岔定理及其在N-S绕流中的应用
A Time-Periodic Bifurcation Theorem and its Application to Navier-Stokes Flow Past an Obstacle
摘要：
本文给出了Banach空间中一个抽象的时间周期分支定理。该方法的关键点以及新颖性在于将原始演化方程分裂成两个不同的耦合方程，一个用于所寻求的解的时间平均，另一个用于“纯周期”分量。这种方法可能是特别有用的研究物理现象发生在无限的空间区域。实际上，我们提供了一个重要的应用定理，通过提供充分条件的时间周期分岔从稳态流动的Navier-Stokes液体过去的三维障碍。
英文摘要：
We show an abstract time-periodic bifurcation theorem in Banach spaces. The key point as well as the novelty of the method is to split the original evolution equation into two different coupled equations, one for the time-average of the sought solution and the other for the "purely periodic" component. This approach may be particularly useful in studying physical phenomena occurring in unbounded spatial regions. Actually, we furnish a significant application of the theorem, by providing sufficient conditions for time-periodic bifurcation from a steady-state flow of a Navier-Stokes liquid past a three-dimensional obstacle.
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