Towards a sufficient criterion for collapse in 3D Euler equations

Abstract

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 H 2( R 3) for infinite time.