ε$\varepsilon$‐Regularity criteria and the number of singular points for the 3D simplified Ericksen–Leslie system

Zhongbao Zuo

Mathematische Nachrichten, 2024, vol. 297, issue 12, 4370-4388

Abstract: In this paper, we consider the partial regularity of suitable weak solution to the 3D simplify Ericksen–Leslie system modeling the hydrodynamical motion of nematic liquid crystal flow, which is a coupled system with the Navier–Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. We present a new regularity criteria for suitable weak solutions to the 3D simplified Ericksen–Leslie system. Moreover, under the condition ∥u∥Ltp,∞Lxq([−1,0]×R3)+∥∇d∥Ltp,∞Lxq([−1,0]×R3):=K

Date: 2024
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https://doi.org/10.1002/mana.202400071

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