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

Barbato, D.; Flandoli, F.; Morandin, F.

doi:10.1090/S0002-9947-2010-05302-4

Energy dissipation and self-similar solutions for an unforced inviscid dyadic model
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by D. Barbato, F. Flandoli and F. Morandin

Trans. Amer. Math. Soc. 363 (2011), 1925-1946

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

Published electronically: November 16, 2010

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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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