论文标题
2D Euler方程的涡旋补丁解决方案的存在和规律性
Existence and Regularity for Vortex Patch Solutions of the 2D Euler Equations
论文作者
论文摘要
在“全球涡流贴片”（Commun。Math。Phys。1993）中，Bertozzi和Constint在级别集合框架中提出了Vortex补丁问题，并证明了此活动标量方程的先验估计。通过扩展用于证明这些估计值的工具，我们构建解决方案并显示出更高的Hölder规律性的传播。这构成了仅在级别框架中进行的涡旋贴片规律性的证明。
In "Global regularity for vortex patches" (Commun. Math. Phys. 1993), Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher Hölder regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.
