A local regularity condition involving two velocity components of Serrin-type for the Navier–Stokes equations.

The present paper deals with the problem of local regularity of weak solutions to the Navier–Stokes equation in Ω × ( 0 , T ) with forcing term f in L 2 . We prove that u is strong in a sub-cylinder Q r ⊂ Ω × ( 0 , T ) if two velocity components u 1 , u 2 satisfy a Serrin-type condition. [ABSTRACT FROM AUTHOR]