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Decay of solutions to dissipative modified quasi-geostrophic equations


Authors: Lucas C. F. Ferreira, César J. Niche and Gabriela Planas
Journal: Proc. Amer. Math. Soc. 145 (2017), 287-301
MSC (2010): Primary 35B40; Secondary 35Q35, 35Q86
DOI: https://doi.org/10.1090/proc/13280
Published electronically: July 25, 2016
MathSciNet review: 3565380
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Abstract: We are concerned with global weak solutions to dissipative modified quasi-geostrophic equations. By employing the Fourier Splitting method, we show time-polynomial decay of solutions for certain types of $ L^p$-initial data. We also prove decay estimates for the difference between the full solution and the solution to the linear part. Our results cover, in particular, the supercritical range of the fractional diffusion.


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Additional Information

Lucas C. F. Ferreira
Affiliation: Departamento de Matemática, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda, 651, 13083-859, Campinas - SP, Brazil
Email: lcff@ime.unicamp.br

César J. Niche
Affiliation: Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, CEP 21941-909, Rio de Janeiro - RJ, Brazil
Email: cniche@im.ufrj.br

Gabriela Planas
Affiliation: Departamento de Matemática, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda, 651, 13083-859, Campinas - SP, Brazil
Email: gplanas@ime.unicamp.br

DOI: https://doi.org/10.1090/proc/13280
Keywords: Asymptotic behavior, active scalar equation, Fourier Splitting method
Received by editor(s): March 20, 2016
Published electronically: July 25, 2016
Additional Notes: The authors were partially supported by CNPq, Brazil
The first author was also supported by FAPESP, Brazil
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society