Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 48, Issue 6, Pages 3907-3930Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1048963
Keywords
isentropic Navier-Stokes system; isentropic Euler system; inviscid limit; Korn inequality; Poincare inequality
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Funding
- European Research Council under the European Union's Seventh Framework Programme /ERC [320078]
- RVO [67985840]
- NSF [DMS-1406730]
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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-Poincare inequality on thin channels that may be of independent interest.
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