$L_{3,\infty}$-solutions of the Navier--Stokes equations and backward uniqueness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 58 (2003) no. 2, pp. 211-250

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It is shown that the $L_{3,\infty}$-solutions of the Cauchy problem for the three-dimensional Navier–Stokes equations are smooth.
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L. Escauriaza; G. A. Seregin; V. Šverak. $L_{3,\infty}$-solutions of the Navier--Stokes equations and backward uniqueness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 58 (2003) no. 2, pp. 211-250. http://geodesic.mathdoc.fr/item/RM_2003_58_2_a0/