It is proved that if u is a suitable weak solution to the three-dimensional Navier–Stokes equations from the space\( {L}_{\infty}\left(0,T;{\dot{B}}_{\infty, \infty}^{-1}\right) \), then all scaled energy quantities of u are bounded. As a consequence, it is shown that any axially symmetric suitable weak solution u, belonging to \( {L}_{\infty}\left(0,T;{\dot{B}}_{\infty, \infty}^{-1}\right) \), is smooth.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 477, 2018, pp. 119–128.
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Seregin, G., Zhou, D. Regularity of Solutions to the Navier–Stokes Equations in \( {\dot{B}}_{\infty, \infty}^{-1} \). J Math Sci 244, 1003–1009 (2020). https://doi.org/10.1007/s10958-020-04670-y
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DOI: https://doi.org/10.1007/s10958-020-04670-y