Displaying similar documents to “Statistically stationary solutions to the 3-D Navier-Stokes equation do not show singularities.”

On the instantaneous spreading for the Navier–Stokes system in the whole space

Lorenzo Brandolese, Yves Meyer (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the spatial behavior of the velocity field u ( x , t ) of a fluid filling the whole space n ( n 2 ) for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions u h ( x , t ) u k ( x , t ) d x = c ( t ) δ h , k under more general assumptions on the localization of u . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.

Conditions implying regularity of the three dimensional Navier-Stokes equation

Stephen Montgomery-Smith (2005)

Applications of Mathematics

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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 Foiaş, Guillopé and Temam.

Interior regularity of weak solutions to the perturbed Navier-Stokes equations

Pigong Han (2012)

Applications of Mathematics

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In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771–831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr....