Towards a sufficient criterion for collapse in 3D Euler equations

E. A. Kuznetsov

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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(R3) for infinite time.

Original languageEnglish
Pages (from-to)266-275
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Issue number1-4
Publication statusPublished - 1 Oct 2003
Externally publishedYes


  • 3D Euler equation
  • Blow-up solution
  • Sobolev space


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