HackerPapers

arXiv:1709.10033math.AP

Nonuniqueness of weak solutions to the Navier-Stokes equation

Tristan Buckmaster, Vlad Vicol

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 Holder 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.

arXiv comments
36 pages; minor corrections per referee comments; version accepted by Annals of Mathematics
Journal reference
DOI
Subjects
math.APAnalysis of PDEs math-phMathematical Physics

On Hacker News

Linked by 2 identifiable commenters in 2 comments across 2 threads, from Dec 2017 to Jan 2018.

Comments linking this paper, per year.

Discussed in comments2 threads

  1. What Makes the Hardest Equations in Physics So Difficult? 1 comment

    • Deterministic Chaos is a real bastard. There was a disturbing result a while back about the Navier-Stokes equations in which the existence of non-unique solutions was shown: https://arxiv.org/abs/1709.10033

      hprotagonistView on HNParent context

  2. Mathematicians Find Wrinkle in Famed Fluid Equations 1 comment

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.