New Regularity Criteria for Weak Solutions to the MHD Equations in Terms of an Associated Pressure

Jiří Neustupa, Minsuk Yang

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3 Citations (Scopus)


We assume that Ω is either a smooth bounded domain in R3 or Ω = R3, and Ω is a sub-domain of Ω. We prove that if 0 ≤ T1< T2≤ 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 × (T1, T2). If b≡ 0 then our result generalizes some previous known results from the theory of the Navier–Stokes equations.

Original languageEnglish
Article number73
JournalJournal of Mathematical Fluid Mechanics
Issue number3
Publication statusPublished - 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


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