On the borderline regularity criterion in anisotropic Lebesgue spaces of the Navier-Stokes equations

In this paper, we are concerned with the critical mixed norm regularity of Leray-Hopf weak solutions of the Navier-Stokes equations in three dimensions and higher dimensions. It is shown that u is an element of L-infinity(0, T; (L-q) over right arrow (R-n)) with Sigma(n)(i=1) 1/qi = 1 ensure that Leray-Hopf weak solutions are regular. A new ingredient is epsilon-regularity criterion derived by the De Giorgi iteration technique under this critical regularity in high spatial dimension. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.