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New regularity criteria for weak solutions to the MHD equations in terms of an associated pressure
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SYSNO ASEP 0543473 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title New regularity criteria for weak solutions to the MHD equations in terms of an associated pressure Author(s) Neustupa, Jiří (MU-W) RID, SAI, ORCID
Yang, M. (KR)Article number 73 Source Title Journal of Mathematical Fluid Mechanics. - : Springer - ISSN 1422-6928
Roč. 23, č. 3 (2021)Number of pages 24 s. Language eng - English Country CH - Switzerland Keywords MHD equations ; Navier-Stokes equations ; pressure ; regularity Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA19-04243S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000662934400001 EID SCOPUS 85108059152 DOI 10.1007/s00021-021-00597-9 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1007/s00021-021-00597-9
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