Work

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

Year: 2024

Type: article

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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1549

Authors: Claudia García, Javier Gómez-Serrano

Institutions: Universidad de Granada, Universitat de Barcelona, Brown University, Centre de Recerca Matemàtica

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404115257

FWCI: 0.768

Cites:

Cited by: 1

Related to: 10