New Regularity Criteria for the Navier-Stokes Equations in Terms of Pressure

Abstract

In this paper, we generalize the main results of [1] and [31] to Lorentz spaces, using a simple procedure. The main results are the following. Let n ≥ 3 and let u be a Leray-Hopf solution to the n-dimensional Navier-Stokes equations with viscosity ν and divergence free initial conditionThen there exists a constant c > 0 such that if *