Log Improvement of the Prodi-Serrin Criteria for Navier-Stokes Equations

Abstract

This article is devoted to a Log improvement of Prodi-Serrin criterion for global regularity to solutions to Navier-Stokes equations in dimension 3. It is shown that the global regularity holds under the condition that |u| 5 /(log(1 + |u|)) is integrable in space time variables.