旋转涡斑的边界正则性
Boundary regularity of rotating vortex patches
摘要：
我们证明了一个旋转涡片（或V-状态，在Deem和Zabusky的术语中）的边界是C^infinity类的，只要这个涡片足够接近Lipschitz范数下的分叉圆。如果旋转面片在C^2范数下足够接近分叉圆，则旋转面片是凸的。我们的证明是基于布尔贝的方法V-状态。因此，共形映射起着相关的作用，以及估计，在Hölder空间，某些非卷积奇异积分运营商的Calderón-Zygmund型。
英文摘要：
We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is of class C^infinity provided the patch is close enough to the bifurcation circle in the Lipschitz norm. The rotating patch is convex if it is close enough to the bifurcation circle in the C^2 norm. Our proof is based on Burbea's approach to V-states. Thus conformal mapping plays a relevant role as well as estimating, on Hölder spaces, certain non-convolution singular integral operators of Calderón-Zygmund type.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
