Geodesic
Note on bounded scale-invariant quantities for the Navier–Stokes equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Tome 397 (2011), pp. 150-156 
G. Seregin. Note on bounded scale-invariant quantities for the Navier–Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Tome 397 (2011), pp. 150-156. http://geodesic.mathdoc.fr/item/ZNSL_2011_397_a7/
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     title = {Note on bounded scale-invariant quantities for the {Navier{\textendash}Stokes} equations},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_397_a7/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this note, we show that if the velocity field $v\in L_\infty(BMO^{-1})$, then all scaled energy quantities are bounded. An interesting consequence is that each axially symmetric solution to the Navier–Stokes belonging to $L_\infty(BMO^{-1})$ is smooth.

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