Authors: Ahmad M. Alghamdi ; Sadek Gala ; Maria Alessandra Ragusa

In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion via the gradient of one velocity component in multiplier spaces.

• 35K15 - Initial value problems for second-order parabolic equations
• 35Q30 - Navier-Stokes equations
• 76D03 - Existence, uniqueness, and regularity theory for incompressible viscous fluids