78935 20230914083229.0 doi 10.1155/2019/4763450 sideral 111273 ART-2019-111273 eng Abadias, L. Universidad de Zaragoza (orcid)0000-0003-2453-7841 Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators 2019 Access copy available to the general public Unrestricted In this paper we treat the following partial differential equation, the quasigeostrophic equation: d / dt + u · grad f = - s - A a f, 0 = a = 1, where (A, D (A)) is the infinitesimal generator of a convolution C 0 -semigroup of positive kernel on L p (R n), with 1 = p < 8. Firstly, we give remarkable pointwise and integral inequalities involving the fractional powers (- A) a for 0 = a = 1. We use these estimates to obtain L p -decayment of solutions of the above quasigeostrophic equation. These results extend the case of fractional derivatives (taking A = ¿, the Laplacian), which has been studied in the literature. info:eu-repo/grantAgreement/ES/DGA/E26-17R info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.896 2019 MATHEMATICS, APPLIED 50 / 260 = 0.192 2019 Q1 T1 MATHEMATICS 24 / 323 = 0.074 2019 Q1 T1 0.455 2019 Analysis 2019 Q3 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Miana, P.J. Universidad de Zaragoza (orcid)0000-0001-9430-343X 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 2019, 4763450 (2019), [7 pp] j. funct. spaces Journal of Function Spaces 2314-8896 578793 http://zaguan.unizar.es/record/78935/files/texto_completo.pdf Versión publicada 84264 http://zaguan.unizar.es/record/78935/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:78935 articulos driver 2023-09-13-10:43:53 ARTICLE