Details

Autor(en) / Beteiligte

• Cao, Daomin
• Qin, Guolin
• Zhan, Weicheng
• Zou, Changjun

Titel

Global solutions for the generalized SQG equation and rearrangements

Ist Teil von

• Transactions of the American Mathematical Society, 2023-03, Vol.376 (3), p.2181-2211

Erscheinungsjahr

2023

Quelle

American Mathematical Society Publications

Beschreibungen/Notizen

• In this paper, we study the existence of rotating and traveling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation. The solutions are obtained by maximization of the energy over the set of rearrangements of a fixed function. The rotating solutions take the form of co-rotating vortices with N-fold symmetry. The traveling-wave solutions take the form of translating vortex pairs. Moreover, these solutions constitute the desingularization of co-rotating N point vortices and counter-rotating pairs. Some other quantitative properties are also established.