We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier–Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L∞(0 , T; L3 , w(R3)) without any smallness assumption on that scale, where L3 , w(R3) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t.
Bibliographical noteFunding Information:
H. J. Choe has been supported by the National Reserch Foundation of Korea (NRF) grant, funded by the Korea government(MSIP) (No. 2015R1A5A1009350). J. Wolf has been supported by the German Research Foundation (DFG) through the project WO1988/1-1; 612414. M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2015R1A5A1009350) and (No. 2016R1C1B2015731).
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