Solution of the Millennium Problem for the Navier-Stokes Equations

One of the millennium problems can be stated as follows: can there be smooth, not vanishing identically initial data for the Navier-Stokes equations in R such that the corresponding solution to the NSP (Navier-Stokes problem) exists for all times t ≥ 0? We prove that such a solution does not exist.

Publication Details

Journal
Annals of Communications in Mathematics
Published
2025-09-29
DOI
https://doi.org/10.62072/acm.2025.080307
Primary Topic
Computational Fluid Dynamics and Aerodynamics
Type
article
Field-Weighted Citation Impact
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article

Solution of the Millennium Problem for the Navier-Stokes Equations

Annals of Communications in Mathematics
Computational Fluid Dynamics and Aerodynamics
article

Solution of the Millennium Problem for the Navier-Stokes Equations

article en

Abstract

One of the millennium problems can be stated as follows: can there be smooth, not vanishing identically initial data for the Navier-Stokes equations in R such that the corresponding solution to the NSP (Navier-Stokes problem) exists for all times t ≥ 0? We prove that such a solution does not exist.

Annals of Communications in Mathematics
Openalex Percentile: Top 72%
Computational Fluid Dynamics and Aerodynamics
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Solution of the Millennium Problem for the Navier-Stokes Equations · Annals of Communications in Mathematics (2025) | TGRS Research Map | TGRS