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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

  • Czech description

Classification

  • 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

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