Regularity Criterion for Weak Solutions to the Navier-Stokes Equations in Terms of the Gradient of the Pressure.

The article examines the regularity criterion for weak solutions to the Navier-Stokes equations in terms of the gradient of the pressure. An interpolation inequality was used to refine when the solution is smooth. Deriving a priori estimates for smooth solutions is measured through multiplying the regularity condition of weak solutions to the Navier-Stokes equations by the interpolation inequality. Since the Leray weak solution satisfies the energy inequality, Serrin's uniqueness criterion can be applied.