Statistically Stationary Solutions to the 3D Navier-Stokes Equations do not show Singularities

Franco Flandoli (Università di Pisa)
Marco Romito (Università di Firenze)


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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Pages: 1-15

Publication Date: August 17, 2001

DOI: 10.1214/EJP.v6-78


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