One component regularity for the Navier–Stokes equations

171 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On the regularity of the solutions of the Navier–Stokes equations via one velocity component (2010, background): “we are not so far away from 2 t + 3 s = 2 which ensures the regularity if ∇u ∈ L(0, T ; Ls(R3)) (but also if only either ∇3u belongs to this space—see [8]—or only ∂u2 ∂x2 and ∂u3 ∂x3 , see [12]).”
Regularity Criteria for the Three-dimensional Navier-Stokes Equations (2008, background): “In addition, some other sufficient regularity conditions were established in terms of only one component of the velocity field of the 3D NSE on the whole space R 3 or under periodic boundary conditions (cf. e.g., [20], [23], [35], [46]).”