论文标题
周期性和准周期性Euler- $α$流靠近Rankine涡流
Periodic and quasi-periodic Euler-$α$ flows close to Rankine vortices
论文作者
论文摘要
在目前的贡献中，我们首先证明存在$ \ mathbf {m} $ - 折叠的简单连接的V型状态，靠近Euler- $α$方程的单位光盘。这些溶液被隐式获得为圆形斑块的分叉曲线。我们还证明，如果比例参数$α$属于合适的类似cantor的一组几乎完整的lebesgue Mouse，则在时间涡流贴片中存在准周期性。用于证明这一结果的技术是从berti-bolle理论中借用的，在pdes的KAM背景下。
In the present contribution, we first prove the existence of $\mathbf{m}$-fold simply-connected V-states close to the unit disc for Euler-$α$ equations. These solutions are implicitly obtained as bifurcation curves from the circular patches. We also prove the existence of quasi-periodic in time vortex patches close to the Rankine vortices provided that the scale parameter $α$ belongs to a suitable Cantor-like set of almost full Lebesgue measure. The techniques used to prove this result are borrowed from the Berti-Bolle theory in the context of KAM for PDEs.
