New regularity criteria for weak solutions to the MHD equations in terms of an associated pressure

0543473 - MÚ 2022 RIV CH eng J - Journal Article
Neustupa, Jiří - Yang, M.
New regularity criteria for weak solutions to the MHD equations in terms of an associated pressure.
Journal of Mathematical Fluid Mechanics. Roč. 23, č. 3 (2021), č. článku 73. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : MHD equations * Navier-Stokes equations * pressure * regularity
OECD category: Pure mathematics
Impact factor: 1.907, year: 2021
Method of publishing: Limited access
https://doi.org/10.1007/s00021-021-00597-9

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.
Permanent Link: http://hdl.handle.net/11104/0320665