arXiv 0811.16892008-11-11math.AP

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

D. Barbato, F. Flandoli, F. Morandin

备注：: 30 pages, submitted to Trans. Amer. Math. Soc

英文摘要：

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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