Nonuniqueness of weak solutions to the Navier-Stokes equation

Tristan Buckmaster, Vlad Vicol

Research output: Contribution to journalArticle

Abstract

For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Hölder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions of the 3D Navier-Stokes equations.

Original languageEnglish (US)
Pages (from-to)101-144
Number of pages44
JournalAnnals of Mathematics
Volume189
Issue number1
DOIs
StatePublished - 2019

Keywords

  • Convex integration
  • Euler equations
  • Intermittency
  • Inviscid limit
  • Navier-Stokes
  • Turbulence
  • Weak solutions

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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