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MiS Preprint
79/2015

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

Peter Bella, Eduard Feireisl, Marta Lewicka and Antonín Novotný

Abstract

We derive the 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 Korn-Poincaré's inequality on thin channels that may be of independent interest.

Received:
Nov 19, 2015
Published:
Nov 30, 2015

Related publications

inJournal
2016 Repository Open Access
Peter Bella, Eduard Feireisl, Marta Lewicka and Antonín Novotný

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

In: SIAM journal on mathematical analysis, 48 (2016) 6, pp. 3907-3930