@article{Li2022, 
author = {Qiang Li and Baoquan Yuan},
title = {A regularity criterion for liquid crystal flows in terms of the component of velocity and the horizontal derivative components of orientation field},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {4168-4175},
keywords = {liquid crystal flow, velocity component, regularity criterion},
url = {https://www.sciopen.com/article/10.3934/math.2022231},
doi = {10.3934/math.2022231},
abstract = {In this paper, we establish a regularity criterion for the 3D nematic liquid crystal flows. More precisely, we prove that the local smooth solution    (  u  ,  d  ) is regular provided that velocity component        u          3      , vorticity component        ω          3       and the horizontal derivative components of the orientation field        ∇          h        d satisfy                                 ∫                      0                                T                                    |                          |                          u                      3                                    |                                      |                                              L                              p                                                                                        2                p                                            p                −                3                                                    +                  |                          |                          ω                      3                                    |                                      |                                              L                              q                                                                                        2                q                                            2                q                −                3                                                    +                  |                          |                          ∇                      h                          d                  |                                      |                                              L                              a                                                                                        2                a                                            a                −                3                                                              d                t        <        ∞        ,                            w        i        t        h                        3        <        p        ≤        ∞        ,                          3          2                <        q        ≤        ∞        ,                3        <        a        ≤        ∞        .}
}