%0 Journal Article %T Conditions implying regularity of the three dimensional Navier-Stokes equation %A Stephen Montgomery-Smith %J Mathematics %D 2003 %I arXiv %X We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foias, Guillope and Temam. %U http://arxiv.org/abs/math/0301207v6