发表机构
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas; Departamento de Matemáticas, Universidad Autónoma de Madrid; Departamento de Matemática Aplicada, Universidad de Granada（西班牙高等科学研究院数学科学研究所; 马德里自治大学数学系; 格拉纳达大学应用数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过半-Yamabe方程结合Lyapunov-Schmidt约化，构造出SQG方程的无穷多光滑非径向稳态解，且当顶点数趋于无穷时解收敛到径向轮廓并带低阶涡片修正。
AI 中文摘要
我们证明了具有有限动能的表面准地转（SQG）方程存在无穷多个光滑非径向稳态解。我们的构造基于二维半-Yamabe方程的一族非径向变号解，该族解通过Lyapunov-Schmidt约化得到，集中在正多边形的顶点处。当顶点数趋于无穷时，相关的稳态SQG解收敛到以原点为中心的径向稳态轮廓，同时伴随一个低阶涡片修正项。
英文摘要
We prove the existence of infinitely many smooth nonradial stationary solutions to the surface quasi-geostrophic (SQG) equation with finite kinetic energy. Our construction is based on a family of nonradial sign-changing solutions to the two-dimensional half-Yamabe equation, obtained via a Lyapunov--Schmidt reduction and concentrated at the vertices of a regular polygon. As the number of vertices tends to infinity, the associated stationary SQG solutions converge to a radial stationary profile centered at the origin, together with a lower-order vortex sheet correction.
CommentsMinor changes have been made, including a fix to Lemma 2.1 and small corrections
