| Full text | |
| Author(s): |
Cuba, Edison
;
Ferreira, Lucas c. f.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 57, n. 1, p. 35-pg., 2025-01-01. |
| Abstract | |
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) | |
| FAPESP's process: | 20/05618-6 - Well-posedness and qualitative properties for nonlinear PDEs |
| Grantee: | Lucas Catão de Freitas Ferreira |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 21/10769-6 - Well-posedness and regularity theory for nonlocal and nonlinear problems |
| Grantee: | Edison Fausto Cuba Huamani |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |