Towards a sufficient criterion for collapse in 3D Euler equations

Details Towards a sufficient criterion for collapse in 3D Euler equations Towards a sufficient criterion for collapse in 3D Euler equations

2002-04-26

arxiv.org/abs/physics/0204080v1

Physics

Fluid Dynamics

Scientific paper

10.1016/S0167-2789(03)00225-2

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 can not be continued in the Sobolev space $H^2({\cal R}^3)$ for infinite time.

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