2008/11/11 by Barbato, D., Flandoli, F., Morandin, F.
#35Q30 #35Q35 #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.0811.1689
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.