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- Title
A REGULARITY CRITERION FOR THE NAVIER-STOKES EQUATIONS IN TERMS OF THE HORIZONTAL DERIVATIVES OF THE TWO VELOCITY COMPONENTS.
- Authors
WENYING CHEN; GALA, SADEK
- Abstract
In this article, we consider the regularity for weak solutions to the Navier-Stokes equations in R³. It is proved that if the horizontal derivatives of the two velocity components ∇h ũ ∈ L²/(2-r)(0, T; Ṁ ₂, ₃ /r(R³)), for 0 < r < 1, then the weak solution is actually strong, where Ṁ²,³/r is the critical Morrey-Campanato space and ũ = (u ₁, u ₂, 0), ∇h ũ = (∂ ₁u₁,∂u₂u₂, 0).
- Subjects
NAVIER-Stokes equations; GENERALIZED spaces; SPEED; MATHEMATICAL analysis; EQUATIONS; MATHEMATICAL models
- Publication
Electronic Journal of Differential Equations, 2011, Vol 2011, p1
- ISSN
1550-6150
- Publication type
Article