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We formulate a new criterion for regularity of a suitable weak solution v tothe Navier-Stokes equations at the space-time point (x_0,t_0). The criterionimposes a Serrin-type integrability condition on v only in a backwardneighbourhood of (x_0,t_0), intersected with the exterior of a certainspace-time paraboloid with vertex at point (x_0,t_0). We make no specialassumptions on the solution in the interior of the paraboloid.

archive for rational mechanics and analysis

A Refinement of the Local Serrin--Type Regularity A refinement of the  local Serrin--type regularity criterion for a suitable weak solution to the  Navier--Stokes equations