A Regularity Criterion for the Weak Solutions to the Navier–Stokes–Fourier System
✍ Scribed by Feireisl, Eduard; Novotný, Antonín; Sun, Yongzhong
- Book ID
- 125341549
- Publisher
- Springer
- Year
- 2013
- Tongue
- English
- Weight
- 258 KB
- Volume
- 212
- Category
- Article
- ISSN
- 0003-9527
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## Abstract Consider the nonstationary Navier–Stokes equations in Ω × (0, __T__), where Ω is a bounded domain in ℝ^3^. We prove interior regularity for suitable weak solutions under some condition on the pressure in the class of scaling invariance. The notion of suitable weak solutions makes it pos
In this paper, we consider the regularity criterion of axisymmetric weak solutions to the Navier-Stokes equations in R 3 . Let u be an axisymmetric weak solution in R 3 × (0, T ), w = curl u, and w θ be the azimuthal component of w in the cylindrical coordinates. It is proved that u becomes a regula