@article{Wang2026, 
author = {Jinhuan Wang and Yongsheng Nie},
title = {On conditional regularity criteria for the 3D generalized MHD system via partial components},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {5},
pages = {3315-3333},
keywords = {generalized MHD equations, regularity criterion, partial components, weak solutions},
url = {https://www.sciopen.com/article/10.3934/era.2026149},
doi = {10.3934/era.2026149},
abstract = {This paper focuses on the regularity criteria for the 3D generalized magnetohydrodynamic (MHD) equations, particularly those involving the partial components of the velocity        u    3   and the magnetic field    (      b    1    ,      b    2    ,      b    3    ). For any    l  ,  i  ,  j  ,  k  ∈  {  1  ,  2  ,  3  }, we establish regularity criteria via        ∂    l        u    3   and    (      ∂    i        b    1    ,      ∂    j        b    2    ,      ∂    k        b    3    ),        u    3   and    (      ∂    i        b    1    ,      ∂    j        b    2    ,      ∂    k        b    3    ), or        ∂    l        u    3   and    (      b    1    ,      b    2    ,      b    3    ). Furthermore, a comprehensive regularity condition is obtained via    (  ξ      u    3    ,  η      b    1    ,  ζ      b    2    ,  σ      b    3    ) and    (  ξ                  ′            ∂          l            u    3    ,  η                  ′            ∂          i            b    1    ,  ζ                  ′            ∂          j            b    2    ,  σ                  ′            ∂          k            b    3    ) with    ξ  +  ξ                  ′        =  η  +  η                  ′        =  ζ  +  ζ                  ′        =  σ  +  σ                  ′        =  1 and    ξ  ,  η  ,  ζ  ,  σ  ,  ξ                  ′        ,  η                  ′        ,  ζ                  ′        ,  σ                  ′        ∈  {  0  ,  1  }.}
}