Despite much effort, the question of whether the Navier–Stokes equations allow solutions that develop singularities in finite time remains unresolved. Terence Tao discusses the problem, and possible routes to a solution.
Access options
Subscribe to Journal
Get full journal access for 1 year
111,86 €
only 9,32 € per issue
All prices include VAT for Germany.
Rent or Buy article
Get time limited or full article access on ReadCube.
from$8.99
All prices are NET prices.
References
- 1.
Fefferman, C. in The Millennium Prize Problems (eds Carlson, J., Jaffe, A. & Wiles, A.) 57–67 (Clay Mathematics Institute, 2006).
- 2.
Kolmogorov, A. N. Dissipation of energy in locally isotropic turbulence [Russian]. Dokl. Akad. Nauk SSSR 32, 16–18 (1941); English translation available in Levin, V. Proceedings: Mathematical and Physical Sciences (Turbulence and Stochastic Process: Kolmogorov’s Ideas 50 Years On) Vol. 434 15–17 (Royal Society, 1991).
- 3.
Nečas, J., Růžička, M. & Šverák, V. On Leray’s self-similar solutions of the Navier–Stokes equations. Acta Math. 176, 283–294 (1996).
- 4.
Tao, T. Finite time blowup for an averaged three-dimensional Navier–Stokes equation. J. Amer. Math. Soc. 29, 601–674 (2016).
- 5.
Tao, T. On the universality of potential well dynamics. Dynam. Part. Differ. Eq. 14, 219–238 (2017).
- 6.
Tao, T. On the universality of the incompressible Euler equation on compact manifolds. Discrete Contin. Dyn. Syst. Ser. A. 38, 1553–1565 (2018).
- 7.
Tao, T. On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows. Preprint at arXiv https://arxiv.org/abs/1902.06313 (2019).
Author information
Ethics declarations
Competing interests
The author declares no competing interests.
Rights and permissions
About this article
Cite this article
Tao, T. Searching for singularities in the Navier–Stokes equations. Nat Rev Phys 1, 418–419 (2019) doi:10.1038/s42254-019-0068-9
Published
Issue Date
DOI
