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A pressure associated with a weak solution to the Navier-Stokes equations with Navier's boundary conditions
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SYSNO ASEP 0525121 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A pressure associated with a weak solution to the Navier-Stokes equations with Navier's boundary conditions Author(s) Neustupa, Jiří (MU-W) RID, SAI, ORCID
Nečasová, Šárka (MU-W) RID, SAI, ORCID
Kučera, Petr (MU-W) SAIArticle number 37 Source Title Journal of Mathematical Fluid Mechanics. - : Springer - ISSN 1422-6928
Roč. 22, č. 3 (2020)Number of pages 20 s. Language eng - English Country CH - Switzerland Keywords Navier-Stokes equations ; Navier’s slip boundary conditions ; weak solutions ; associated pressure Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA17-01747S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000540799900008 EID SCOPUS 85086081392 DOI 10.1007/s00021-020-00500-y Annotation We show that if u is a weak solution to the Navier–Stokes initial–boundary value problem with Navier’s slip boundary conditions in QT:=Ω×(0,T), where Ω is a domain in R3, then an associated pressure p exists as a distribution with a certain structure. Furthermore, we also show that if Ω is a “smooth” domain in R3 then the pressure is represented by a function in QT with a certain rate of integrability. Finally, we study the regularity of the pressure in sub-domains of QT, where u satisfies Serrin’s integrability conditions. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2021 Electronic address https://doi.org/10.1007/s00021-020-00500-y
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