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Conditions Implying Regularity of the Three Dimensional Navier-Stokes Equation

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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 Foias, Guillope and Temam.

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The author was partially supported by an NSF grant.

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Montgomery-Smith, S. Conditions Implying Regularity of the Three Dimensional Navier-Stokes Equation. Appl Math 50, 451–464 (2005).

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