EXISTENCE OF ASYMMETRIC VORTEX PATCH FOR THE GENERALIZED SQG EQUATIONS

Autor(es)

Cuba, Edison ; Ferreira, Lucas c. f.

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 57, n. 1, p. 35-pg., 2025-01-01.

Resumo

This paper aims to study the existence of asymmetric solutions for the twodimensional generalized surface quasi-geostrophic (gSQG) equations of simply connected patches for \alpha \in [1, 2) in the whole plane, where \alpha = 1 corresponds to the surface quasi-geostrophic equations (SQG). More precisely, we construct nontrivial simply connected co-rotating and traveling patches with unequal vorticity magnitudes. The proof is carried out by means of a combination of a desingularization argument with the implicit function theorem on the linearization of contour dynamics equation. Our results extend recent ones in the range \alpha \in [0, 1) by Hassainia and Hmidi [Discrete Contin. Dyn. Syst., 41 (2021), pp. 1939--1969] and Hassainia and Wheeler [SIAM J. Math. Anal., 54 (2022), pp. 6054--6095] to more singular velocities, filling an open gap in the range of alpha . (AU)

• Processo FAPESP: 20/05618-6 - Boa-colocação e propriedades qualitativas para EDPs não-lineares
• Beneficiário: Lucas Catão de Freitas Ferreira
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 21/10769-6 - Teoria de boa colocação e regularidade para problemas não locais e não lineares
• Beneficiário: Edison Fausto Cuba Huamani
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado