In this note we establish a Serrin-type regularity criterion in terms of pressure for Leray weak solutions to the Navier-Stokes equation in R d . Here we call u a Leray weak solution if u is a weak solution of finite energy, i.e. It is known that if a Leray weak solution u belongs to then u is reg
A regularity criterion for the Navier–Stokes equations with mass diffusion
✍ Scribed by Yong Zhou; Jishan Fan
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 205 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
In this work, a regularity criterion is proved for local strong solutions of the Navier-Stokes equations in the presence of mass diffusion.
📜 SIMILAR VOLUMES
## 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
## Communicated by M. Costabel In this work, we improved the regularity criterion on the Cauchy problem for the Navier-Stokes equations in multiplier space in terms of the two partial derivatives of velocity fields, @ 1 u 1 and @ 2 u 2 .