If $mu$ is a probability measure on the set of suitable weak solutions of the 3D Navier-Stokes equations, invariant for the time-shift, with finite mean dissipation rate, then at every time t the set of singular points is empty $mu$-a.s. The existence of a measure $mu$ with the previous properties is also proved; it may describe a turbulent asymptotic regime.
Statistically Stationary Solutions to the 3D Navier-Stokes Equations do not show Singularities / F. FLANDOLI; M. ROMITO. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - ELETTRONICO. - 6:(2001), pp. 0-0.
Statistically Stationary Solutions to the 3D Navier-Stokes Equations do not show Singularities
ROMITO, MARCO
2001
Abstract
If $mu$ is a probability measure on the set of suitable weak solutions of the 3D Navier-Stokes equations, invariant for the time-shift, with finite mean dissipation rate, then at every time t the set of singular points is empty $mu$-a.s. The existence of a measure $mu$ with the previous properties is also proved; it may describe a turbulent asymptotic regime.
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