Anisotropic Prodi–Serrin regularity criteria for the 3D Navier–Stokes equations involving the gradient of one velocity component

Abstract

In this paper, we prove some optimal regularity criteria for the 3D incompressible Navier–Stokes equations involving the gradient of one velocity component in the framework of anisotropic Lebesgue spaces satisfying Prodi–Serrin condition. These results cover the previous ones established by Wolf (2015) and O (2023).