## Abstract In this paper, we exclude the possibility of existence of a singular solution of the selfsimilar type proposed by Jean Leray More precisely, using a slightly stronger hypothesis we give a simpler proof to the analogous result established by J. Nečas, M. Rúžička and V. Šverák. We also di
On the Dimension of the Singular Set of Solutions to the Navier–Stokes Equations
✍ Scribed by James C. Robinson; Witold Sadowski
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 180 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0010-3616
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We consider suitably weak solutions (u, p) to the incompressible Navier Stokes equations and under various assumptions on u obtain estimates for the size of its singular set. One of our results improves a well known theorem of Caffarelli, Kohn, and Nirenberg.
## Abstract We consider a suitable weak solution to the three‐dimensional Navier‐Stokes equations in the space‐time cylinder Ω × ]0, __T__[. Let Σ be the set of singular points for this solution and Σ (__t__) ≡ {(__x, t__) ∈ Σ}. For a given open subset ω ⊆ Ω and for a given moment of time __t__ ∈]0