2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173860A 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.30 pages, submitted to Trans. Amer. Math. SocAnalysis of PDEs35Q30, 35Q35, 76B03text