Abstract
In this note we prove a logarithmically improved regularity criterion in terms of the Besov space norm for the Navier–Stokes equations. The result shows that if a mild solution u satisfies \({\int_{0}^{T}\frac{\|u (t,\cdot)\|_{{\dot{B}}_{\infty,\infty}^{-r}}^{\frac{2}{1-r}}}{1+\ln(e+\| u(t,\cdot)\|_{H^{s}})}\text{d}t < \infty}\) for some 0 ≤ r < 1 and \({s\geq\frac{n}{2}-1}\) , then u is regular at t = T.
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Communicated by Adrian Constantin.
Research supported by the National Natural Science Foundation of China (10771223).
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Liu, Q., Zhao, J. & Cui, S. A logarithmically improved regularity criterion for the Navier–Stokes equations. Monatsh Math 167, 503–509 (2012). https://doi.org/10.1007/s00605-011-0313-5
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DOI: https://doi.org/10.1007/s00605-011-0313-5