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

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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. 
@article{ZNSL_2011_397_a7,
     author = {G. Seregin},
     title = {Note on bounded scale-invariant quantities for the {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--156},
     publisher = {mathdoc},
     volume = {397},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_397_a7/}
}
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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/