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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Energy dissipation and self-similar solutions for an unforced inviscid dyadic model


Authors: D. Barbato, F. Flandoli and F. Morandin
Journal: Trans. Amer. Math. Soc. 363 (2011), 1925-1946
MSC (2010): Primary 35Q35, 76B03, 35Q30
Published electronically: November 16, 2010
MathSciNet review: 2746670
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Abstract: A shell-type model of an inviscid fluid, previously considered in the literature, is investigated in absence of external force. Energy dissipation of positive solutions is proved, and decay of energy like $ t^{-2}$ is established. Self-similar decaying positive solutions are introduced and proved to exist and classified. Coalescence and blow-up are obtained as a consequence, in the class of arbitrary sign solutions.


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Additional Information

D. Barbato
Affiliation: Dipartimento di Matematica Pura e Applicata, Università\ degli Studi di Padova, Via Treste 63, 35121 Padova, Italy

F. Flandoli
Affiliation: Department of Applied Mathematics, University of Pisa, Via Buonarroti 1, 56127 Pisa, Italy

F. Morandin
Affiliation: Department of Mathematics, University of Parma, Parco Scienze 53A, 43124 Parma, Italy

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05302-4
PII: S 0002-9947(2010)05302-4
Received by editor(s): October 30, 2008
Published electronically: November 16, 2010
Article copyright: © Copyright 2010 American Mathematical Society