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

DOI:
https://doi.org/10.1090/S0002-9947-2010-05302-4

Published electronically:
November 16, 2010

MathSciNet review:
2746670

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 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:
https://doi.org/10.1090/S0002-9947-2010-05302-4

Received by editor(s):
October 30, 2008

Published electronically:
November 16, 2010

Article copyright:
© Copyright 2010
American Mathematical Society