论文标题
两倍双连接的均匀旋转涡流贴片的分叉的分叉
Degenerate bifurcations of two-fold doubly-connected uniformly rotating vortex patches
论文作者
论文摘要
在本文中，我们获得了由二-D不可压缩的Euler方程的两倍双连接均匀旋转的涡旋斑块的家族。主要困难来自问题的强烈退化，线性化的内核都不是一维的，也不是transeversallity条件。为此，我们对非线性功能进行了详细的分析，并通过扰动由截短多项式定义的实际代数品种来获得分叉曲线。此外，我们的结果部分回答了Hmidi和Mateu在\ cite {hmidi2016a}中提出的问题（\ emph {adv.math.302（2016），799-850}）。
In this paper, we obtain families of two-fold doubly-connected uniformly rotating vortex patches of the 2-D incompressible Euler equations emanating from some specific annuli. The main difficulty comes from strong degeneracy of the problem, neither the kernel of linearization is one-dimensional nor the transeversallity condition holds. To this end, we make a detailed analysis on the nonlinear functional and the bifurcation curves are obtained by perturbing real algebraic varieties defined by truncated polynomials. In addition, our result partially answers an problem proposed by Hmidi and Mateu in \cite{Hmidi2016a} (\emph{Adv.Math.302 (2016), 799-850}).
