A New Criterion for Partial Regularity of Suitable Weak Solutions to the Navier-Stokes Equations

In the present paper we study local properties of suitable weak solutions to the Navier-Stokes equation in a cylinder Q = Omega x (0, T). Using the local representation of the pressure we are able to define a positive constant e, such that for every parabolic subcylinder Q(R) subset of Q the condition R-2 integral(QR) vertical bar u vertical bar(3) dxdt <= epsilon(*) implies u is an element of L-infinity(Q(R/2)). As one can easily check this condition is weaker then the well known Serrin's condition as well as the condition introduced by Farwig, Kozono and Sohr. Since our condition can be verified for suitable weak solutions to the Navier-Stokes system it improves the known results substantially.