https://doi.org/10.1140/epjp/s13360-022-02362-x
Regular Article
Regularity for 3D MHD equations in Lorentz space
School of Mathematic Sciences, Fudan University, 200433, Shanghai, China
Received:
23
October
2021
Accepted:
7
January
2022
Published online:
31
January
2022
We shall consider the regularity for 3D MHD equations in this paper. When the velocity field is bounded in a critical space and the magnetic field satisfies a weaker condition, it can be concluded that the weak solution of MHD equation is a smooth solution. We prove that the weak solutions are Hölder continuous if the velocity field belongs to some Lorentz space and the magnetic field belongs to a bigger space than Lorentz space, that is the magnetic field satisfies an even weaker condition than the velocity filed. Our main mathematical tool is the backward uniqueness theory for the parabolic operators established by Escauriaza, Seregin and 
ver
k.
This work was supported partly by NSFC grant 11971113, 11631011, 12161077.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
