Dissipative Euler Flows with Onsager-Critical Spatial Regularity

Tristan Buckmaster, Camillo De Lellis, László Székelyhidi

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


For any ɛ > 0 we show the existence of continuous periodic weak solutions v of the Euler equations that do not conserve the kinetic energy and belong to the space (Formula presented.) ; namely, x ↦ v (x,t) is ⅓−ε-Hölder continuous in space at a.e. time t and the integral (Formula presented.) is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class (Formula presented.).

Original languageEnglish (US)
Pages (from-to)1613-1670
Number of pages58
JournalCommunications on Pure and Applied Mathematics
Issue number9
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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