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Navier-Stokes equation; vorticity; Prodi-Serrin condition; Beale-Kato-Majda condition; Orlicz norm; stochastic method
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 our methods, we give a different approach to a priori estimates of Foiaş, Guillopé and Temam.
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