We study the partial regularity problem of the incompressible Navier–Stokes equations. A reverse Hölder inequality of velocity gradient with increasing support is obtained under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions v belong to L∞(0,T;L3,w(R3)) where L3,w(R3) denotes the standard weak Lebesgue space.
Bibliographical noteFunding Information:
Hi Jun Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A5A1009350 and No. 2015R1A2A01002708 ). Minsuk Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731 ).
© 2017 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Applied Mathematics