A regularity criterion for the Navier-Stokes equations via two entries of the velocity Hessian tensor

Global Regularity Criterion for the 3d Navier–stokes Equations Involving One Entry of the Velocity Gradient Tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three–dimensional Navier–Stokes equations in the whole space, as well as for the case of periodic boundary conditions. AMS Subject Classifications: 35Q35, 65M70

Navier-Stokes equations with regularity in two entries of the velocity gradient tensor

A comparative study between two numerical solutions of the Navier-Stokes equations

The present study aimed to investigate two numerical solutions of the Navier-Stokes equations. For this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. Solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...

A Regularity Criterion for the Angular Velocity Component in Axisymmetric Navier-stokes Equations

We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].

A Regularity Criterion for the Navier-stokes Equations in Terms of the Horizontal Derivatives of the Two Velocity Components

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 ∇he u ∈ L2/(2−r)(0, T ;Ṁ2,3/r(R)), for 0 < r < 1, then the weak solution is actually strong, where Ṁ2,3/r is the critical MorreyCampanato space and e u = (u1, u2, 0), ∇he u = (∂1u1, ∂2u2, 0).