On the role of pressure in the theory of MHD equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00539554" target="_blank" >RIV/67985840:_____/21:00539554 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.nonrwa.2020.103283" target="_blank" >https://doi.org/10.1016/j.nonrwa.2020.103283</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.nonrwa.2020.103283" target="_blank" >10.1016/j.nonrwa.2020.103283</a>
Alternative languages
Result language
angličtina
Original language name
On the role of pressure in the theory of MHD equations
Original language description
We consider the system of MHD equations in Ω×(0,T), where Ω is a domain in R3 and T>0, with the no slip boundary condition for the velocity u and the Navier-type boundary condition for the magnetic induction b. We show that an associated pressure p, as a distribution with a certain structure, can be always assigned to a weak solution (u,b). The pressure is a function with some rate of integrability if the domain Ω is “smooth”, see section 3. In section 4, we study the regularity of p in a sub-domain Ω1×(t1,t2) of Ω×(0,T), where u (or, alternatively, both u and b) satisfies Serrin's integrability conditions. Regularity criteria for weak solutions to the MHD equations in terms of [Formula presented] are studied in section 5. Finally, section 6 contains remarks on analogous results in the case of Navier's or Navier-type boundary conditions for the velocity u.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
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
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear Analysis: Real World Applications
ISSN
1468-1218
e-ISSN
1878-5719
Volume of the periodical
60
Issue of the periodical within the volume
August
Country of publishing house
GB - UNITED KINGDOM
Number of pages
23
Pages from-to
103283
UT code for WoS article
000633361700024
EID of the result in the Scopus database
2-s2.0-85100195256