Towards a sufficient criterion for collapse in 3D Euler equations

A sufficient integral criterion for a blow-up solution of the Hopf equations (the Euler equations with zero pressure) is found. This criterion shows that a certain positive integral quantity blows up in a finite time under specific initial conditions. Blow up of this quantity means that solution of the Hopf equation in 3D cannot be continued in the Sobolev space H2(R3) for infinite time.