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Abstract
For the generalized surface quasigeostrophic equation {equation presented} 0 < s < 1, we consider for k ≥ 1 the problem of finding a family of kvortex solutions Θ _{ϵ}(x, t) such that as ϵ → 0 {equation presented} for suitable trajectories for the vortices x = ζ _{j}(t). We find such solutions in the special cases of vortices travelling with constant speed along one axis or rotating with same speed around the origin. In those cases the problem is reduced to a fractional elliptic equation which is treated with singular perturbation methods. A key element in our construction is a proof of the nondegeneracy of the radial ground state for the socalled fractional plasma problem {equation presented} whose existence and uniqueness have recently been proven in Chan, del Mar González, Huang, Mainini, and Volzone [Calc. Var. Partial Differential Equations 59 (2020), p. 42].
Original language  English 

Pages (fromto)  66656689 
Number of pages  25 
Journal  Transactions of the American Mathematical Society 
Volume  374 
Issue number  9 
Early online date  9 Jun 2021 
DOIs  
Publication status  Published  31 Dec 2021 
Bibliographical note
Funding Information:Received by the editors August 28, 2020, and, in revised form, February 1, 2021. 2020 Mathematics Subject Classification. Primary 35Q35, 35J61; Secondary 35Q31. The first author was partially supported by NSF of China. The second author was supported by a Royal Society Wolfson Fellowship, UK and Fondecyt grant 1170224, Chile. The third author was supported by a Royal Society Research Professorship, UK. The fourth author was supported by EPSRC research Grant EP/T008458/1. The research of the fifth author was partially supported by NSERC of Canada.
ASJC Scopus subject areas
 General Mathematics
 Applied Mathematics
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 1 Active

Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 31/07/24
Project: Research council