Divergence-conforming B-splines are developed for application to the incompressible
Navier–Stokes equations on geometrically mapped domains. These enable smooth …

In this paper we derive unsteady tri-periodic laminar solutions of the Navier–Stokes
equations. In particular, these represent fully three-dimensional (3-D) flows, since all the …

For the three-dimensional incompressible Navier–Stokes equations, we present a
formulation featuring velocity, vorticity and helical density as independent variables. We find …

Abstract The incompressible Navier-Stokes equations are among the most important partial
differential systems arising from classical physics. They are utilized to model a wide range of …

We present a rigorous numerical analysis and computational tests for the Galerkin finite
element discretization of the velocity-vorticity-helicity formulation of the equilibrium Navier …

We consider the Cauchy problem for the 3D Navier–Stokes equations and show that weak
solutions satisfying suitable geometric conditions are smooth. The first condition we consider …

We review some results concerning the problem of global-in-time regularity for the initial
boundary value problem for the Navier–Stokes equations in three-dimensional domains. In …

In their famous 1993 paper, Constantin and Fefferman consider the evolution Navier–Stokes
equations in the whole space R 3 and prove, essentially, that if the direction of the vorticity is …

We prove geometrically improved version of Prodi–Serrin type blow-up criterion. Let v and ω
be the velocity and the vorticity of solutions to the 3D Navier–Stokes equations and denote …

This short paper presents a simplified and alternative proof of the regularity of weak
solutions to the 3D Navier–Stokes equations with'sufficiently small'jumps in the vorticity …