## Abstract

We assume that Ω is either a smooth bounded domain in R^{3} or Ω = R^{3}, and Ω ^{′} is a sub-domain of Ω. We prove that if 0 ≤ T_{1}< T_{2}≤ T≤ ∞, (u, b, p) is a suitable weak solution of the initial–boundary value problem for the MHD equations in Ω × (0 , T) and either Fγ(p-)∈L∞(T1,T2;L3/2(Ω′)) or Fγ(B+)∈L∞(T1,T2;L3/2(Ω′)) for some γ> 0 , where Fγ(s)=s[ln(1+s)]1+γ, B=p+12|u|2+12|b|2 and the subscripts “−” and “+ ” denote the negative and the nonnegative part, respectively, then the solution (u, b, p) has no singular points in Ω ^{′}× (T_{1}, T_{2}). If b≡ 0 then our result generalizes some previous known results from the theory of the Navier–Stokes equations.

Original language | English |
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Article number | 73 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 23 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2021 Aug |

### Bibliographical note

Funding Information:The first author has been supported by the Academy of Sciences of the Czech Republic (RVO 67985840) and by the Grant Agency of the Czech Republic, grant No. GA19-04243S. The second author acknowledges the support of the National Research Foundation of Korea No. 2021R1A2C4002840 and No. 2015R1A5A1009350.

Publisher Copyright:

© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

## All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics