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A rigorous justification of the Euler and Navier-Stokes equations with geometric effects (1511.06136v1)
Published 19 Nov 2015 in math.AP and physics.flu-dyn
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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