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25 April 2024

» arxiv » 1511.6136

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A rigorous justification of the Euler and Navier-Stokes equations with geometric effects
Peter Bella ; Eduard Feireisl ; Marta Lewicka ; Antonin Novotny ;
Date:	19 Nov 2015
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-Poincare’s inequality on thin channels that may be of independent interest.
Source:	arXiv, 1511.6136
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