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Journal article
On the locally self-similar blowup for the generalized SQG equation
Journal of Differential Equations, v 415, pp 266-302
Jan 2025
Abstract
We analyze finite-time blowup scenarios of locally self-similar type for the inviscid generalized surface quasi-geostrophic equation (gSQG) in R2. Under an Lr growth assumption on the self-similar profile and its gradient, we identify appropriate ranges of the self-similar parameter where the profile is either identically zero, and hence blowup cannot occur, or its Lp asymptotic behavior can be characterized, for suitable r,p. Our results extend the work by Xue [38] regarding the SQG equation, and also partially recover the results proved by Cannone and Xue [3] concerning globally self-similar solutions of the gSQG equation.
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Details
- Title
- On the locally self-similar blowup for the generalized SQG equation
- Creators
- Anne Bronzi - Universidade Estadual de Campinas (UNICAMP)Ricardo Guimarães - Universidade Estadual de Campinas (UNICAMP)Cecilia Mondaini - Department of Mathematics, Drexel University, 3141 Chestnut Street, 19104, Philadelphia, PA, USA
- Publication Details
- Journal of Differential Equations, v 415, pp 266-302
- Publisher
- Elsevier; SAN DIEGO
- Number of pages
- 37
- Grant note
- Sao Paulo Research Foundation (FAPESP): 2019/02512-5, 2018/22385-5, 2022/00948-3 FAEPEX/UNICAMP: 2447/20, 2358/22 NSF: DMS-2009859, DMS-2239325
ACB received support under the grants #2019/02512-5, Sao Paulo Research Foundation (FAPESP) , and #2447/20 and #2358/22, FAEPEX/UNICAMP. RMG received support under the grants #2018/22385-5 and #2022/00948-3, Sao Paulo Research Foundation (FAPESP) . CFM was supported by the grants NSF DMS-2009859 and NSF DMS-2239325. The authors would also like to thank Mimi Dai for helpful comments on an earlier version of this manuscript.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001322203400001
- Scopus ID
- 2-s2.0-85204436707
- Other Identifier
- 991021904811804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics