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Conditions implying regularity of the three dimensional Navier-Stokes equation. (English) Zbl 1099.35086
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.

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
60H30 Applications of stochastic analysis (to PDEs, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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