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arXiv · 1511.06136

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

Peter Bella·Eduard Feireisl·Marta Lewicka·Antonin Novotny
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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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Peter Bella, Eduard Feireisl, Marta Lewicka, Antonin Novotny. 2015-11-19. A rigorous justification of the Euler and Navier-Stokes equations with geometric effects. https://arxiv.org/abs/1511.06136

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