Towards a sufficient criterion for collapse in 3D Euler equations

✍ Scribed by E.A Kuznetsov

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 94 KB
• Volume: 184
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(03)00225-2

✦ Synopsis

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.