主动标量方程双连通同旋行波涡斑的存在性
Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations
摘要：
应用轮廓动力学中的隐函数定理，证明了欧拉方程和广义表面准地转方程的同旋解和行波解的存在性.所得的解构成了点涡的去奇异化。特别地，本文构造的解由双连通分量组成，这与所有已知的结果有本质的不同。
英文摘要：
By applying implicit function theorem on contour dynamics, we prove the existence of co-rotating and travelling patch solutions for both Euler and the generalized surface quasi-geostrophic equation. The solutions obtained constitute a desingularization of points vortices when the size of patch support vanishes. In particular, solutions constructed in this paper consist of doubly connected components, which is essentially different from all known results.
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。
