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A rigorous justification of the Euler and Navier-Stokes equations with geometric effects
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SYSNO ASEP 0466755 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A rigorous justification of the Euler and Navier-Stokes equations with geometric effects Author(s) Bella, P. (DE)
Feireisl, Eduard (MU-W) RID, SAI, ORCID
Lewicka, M. (US)
Novotný, A. (FR)Source Title SIAM Journal on Mathematical Analysis. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0036-1410
Roč. 48, č. 6 (2016), s. 3907-3930Number of pages 24 s. Language eng - English Country US - United States Keywords isentropic Navier-Stokes system ; isentropic Euler system ; inviscid limit Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000391857800010 EID SCOPUS 85007042031 DOI 10.1137/15M1048963 Annotation We derive the one-dimensional (1D) isentropic Euler and Navier--Stokes equations describing the motion of a gas through a nozzle of variable cross section as the asymptotic limit of the 3D isentropic Navier--Stokes system in a cylinder, the diameter of which tends to zero. Our method is based on the relative energy inequality satisfied by any weak solution of the 3D Navier--Stokes system and a variant of the Korn--Poincaré inequality on thin channels that may be of independent interest. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2017
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