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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
A rigorous justification of the Euler and Navier-Stokes equations with geometric effects
Peter Bella, Eduard Feireisl, Marta Lewicka and Antonín NovotnýAbstract
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:
- 19.11.15
- Published:
- 30.11.15