**Stephen Montgomery-Smith, ** **Conditions implying regularity of the three dimensional Navier-Stokes equation.**
*Applications of Mathematics ***50**, (2005), 451-464.
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.
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