论文标题
边界对Euler方程的准周期溶液的出现
Boundary effects on the emergence of quasi-periodic solutions for Euler equations
论文作者
论文摘要
在本文中，我们强调了边界影响对兰金涡流附近的准周期涡流贴片解决方案的构建的重要性，并且由于线性频率的共鸣，其存在在整个空间中未知。通过单位盘中欧拉方程的径向扩张以及使用NASH-MOSER隐式函数迭代方案，我们表明了这种结构的存在，当兰金涡流的半径属于合适的巨大cantor样设置时，我们显示了这种结构的存在。
In this paper, we highlight the importance of the boundary effects on the construction of quasi-periodic vortex patches solutions close to Rankine vortices and whose existence is not known in the whole space due to the resonances of the linear frequencies. Availing of the lack of invariance by radial dilation of Euler equations in the unit disc and using a Nash-Moser implicit function iterative scheme we show the existence of such structures when the radius of the Rankine vortex belongs to a suitable massive Cantor-like set with almost full Lebesgue measure.
