Coupling conditions for the 3x3 Euler system

2009/11/04 by Rinaldo M. Colombo, Colombo, Rinaldo M., Francesca Marcellini +1
Mathematics · #35L65 76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:35L65 #msc:76N10

paper · pdf · doi:10.48550/arxiv.0911.0825

21 pages, 6 figures

arxiv created 2009/11/04 · arxiv updated 2009/12/01

Abstract

This paper is devoted to the extension to the full 3×3 Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct with varying section. First, we consider the Cauchy problem for a pipeline consisting of 2 ducts joined at a junction. Then, this result is extended to more complex pipes. A key assumption in these theorems is the boundedness of the total variation of the pipe's section. We provide explicit examples to show that this bound is necessary.

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