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Article

Montgomery-Smith, Stephen
Conditions implying regularity of the three dimensional Navier-Stokes equation. (English). Applications of Mathematics, vol. 50 (2005), issue 5, pp. 451-464
MSC: 35B65, 35Q30, 46E30, 60H10, 60H30, 76D03, 76D05 | MR 2160072 | Zbl 1099.35086 | DOI: 10.1007/s10492-005-0032-0
Keywords:
Navier-Stokes equation; vorticity; Prodi-Serrin condition; Beale-Kato-Majda condition; Orlicz norm; stochastic method
Summary:
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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