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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00543473" target="_blank" >RIV/67985840:_____/21:00543473 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00021-021-00597-9" target="_blank" >https://doi.org/10.1007/s00021-021-00597-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00021-021-00597-9" target="_blank" >10.1007/s00021-021-00597-9</a>

Result language
angličtina
Original language name
New regularity criteria for weak solutions to the MHD equations in terms of an associated pressure
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-04243S" target="_blank" >GA19-04243S: Partial differential equations in mechanics and thermodynamics of fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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