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arXiv · 2608.00563

Smooth nonradial stationary solutions to SQG via the half-Yamabe equation

Ángel Castro·Antonio J. Fernández·Claudia García
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Abstract

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.

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Ángel Castro, Antonio J. Fernández, Claudia García. 2026-08-01. Smooth nonradial stationary solutions to SQG via the half-Yamabe equation. https://arxiv.org/abs/2608.00563

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