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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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Cite

BibTeXRIS
BibTeX
@misc{castro2026smooth,
  title = {{Smooth nonradial stationary solutions to SQG via the half-Yamabe equation}},
  author = {Ángel Castro and Antonio J. Fernández and Claudia García},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.00563},
  eprint = {2608.00563},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.00563},
}
RIS
TY  - UNPB
TI  - Smooth nonradial stationary solutions to SQG via the half-Yamabe equation
AU  - Ángel Castro
AU  - Antonio J. Fernández
AU  - Claudia García
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2608.00563
UR  - https://arxiv.org/abs/2608.00563
AB  - 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.
ER  -