Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Tristan Buckmaster; Maria Colombo; Vlad Vicol

doi:10.4171/JEMS/1162

Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Tristan Buckmaster, Maria Colombo, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.

Original language	English (US)
Pages (from-to)	3333-3378
Number of pages	46
Journal	Journal of the European Mathematical Society
Volume	24
Issue number	9
DOIs	https://doi.org/10.4171/JEMS/1162
State	Published - 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Navier-Stokes equations
convex integration
non-uniqueness
partial regularity
wild solutions

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10.4171/JEMS/1162

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title = "Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1",

abstract = "We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.",

keywords = "Navier-Stokes equations, convex integration, non-uniqueness, partial regularity, wild solutions",

author = "Tristan Buckmaster and Maria Colombo and Vlad Vicol",

year = "2022",

doi = "10.4171/JEMS/1162",

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AU - Buckmaster, Tristan

AU - Colombo, Maria

AU - Vicol, Vlad

PY - 2022

Y1 - 2022

N2 - We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.

AB - We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.

KW - Navier-Stokes equations

KW - convex integration

KW - non-uniqueness

KW - partial regularity

KW - wild solutions

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Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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