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Self-similar spirals for the generalized surface quasi-geostrophic equations

  • Claudia García

    Universitat de Barcelona, Barcelona, Spain; Universidad de Granada, Granada, Spain

  • Javier Gómez-Serrano

    Universitat de Barcelona, Barcelona, Spain; Centre de Recerca Matemàtica, Bellaterra, Spain; Brown University, Providence, USA
Self-similar spirals for the generalized surface quasi-geostrophic equations cover
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Abstract

We construct a large class of nontrivial (nonradial) self-similar solutions of the generalized surface quasi-geostrophic equations (gSQG). To the best of our knowledge, this is the first rigorous construction of any self-similar solution for these equations. The solutions are of spiral type, locally integrable, and may have mixed sign. Moreover, they bear some resemblance to the finite time singularity scenario numerically proposed by Scott–Dritschel [J. Fluid Mechanics 863, article no. R2 (2019)] in the SQG patch setting.

Cite this article

Claudia García, Javier Gómez-Serrano, Self-similar spirals for the generalized surface quasi-geostrophic equations. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1549