Remarks on a paper by Gavrilov: Grad–Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications

Peter Constantin, Joonhyun La, Vlad Vicol

Research output: Contribution to journalArticle


We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad–Shafranov equations and is inspired by the recent result (Gavrilov in A steady Euler flow with compact support. Geom Funct Anal 29(1):90–197, [Gav19]).

Original languageEnglish (US)
Pages (from-to)1773-1793
Number of pages21
JournalGeometric and Functional Analysis
Issue number6
StatePublished - Dec 1 2019



  • Euler equations
  • Grad–Shafranov
  • MHD equilibrium

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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