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

2015/11/19 by Bella, Peter, Feireisl, Eduard, Lewicka, Marta +1
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.1511.06136

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.

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