Scaling-Invariant Serrin Criterion via One Row of the Strain Tensor for the Navier–Stokes Equations

Abstract

Miller (Arch. Rational Mech. Anal., 2020) posed the question of whether it is possible to prove the Navier–Stokes regularity criterion using only one entry of the strain tensor Sij. Although this paper does not fully address this question, we do establish several scaling-invariant Serrin-type criteria based on one row of the strain tensor.

Keywords

• Navier–Stokes equations
• Serrin-type criteria
• weak solutions
• strain tensor