A rigorous justification of the Euler and Navier-Stokes equations with geometric effects

0466755 - MÚ 2017 RIV US eng J - Journal Article
Bella, P. - Feireisl, Eduard - Lewicka, M. - Novotný, A.
A rigorous justification of the Euler and Navier-Stokes equations with geometric effects.
SIAM Journal on Mathematical Analysis. Roč. 48, č. 6 (2016), s. 3907-3930. ISSN 0036-1410. E-ISSN 1095-7154
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : isentropic Navier-Stokes system * isentropic Euler system * inviscid limit
Subject RIV: BA - General Mathematics
Impact factor: 1.648, year: 2016
http://epubs.siam.org/doi/10.1137/15M1048963

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.
Permanent Link: http://hdl.handle.net/11104/0264991