Blowup in a three‐dimensional vector model for the Euler equations

Abstract

Abstract We present a three‐dimensional vector model given in terms of an infinite system of nonlinearly coupled ordinary differential equations. This model has structural similarities with the Euler equations for incompressible, inviscid fluid flows. It mimics certain important properties of the Euler equations, namely, conservation of energy and divergence‐free velocity. It is proven for certain families of initial data that the model system permits local existence in time for initial conditions in Sobolev spaces H s , s > $5 \over 2$ ; and blowup occurs in the sense that the H 3/2 + ϵ norm becomes unbounded in finite time. © 2004 Wiley Periodicals, Inc.