Compressible Fluids Interacting with a Linear-Elastic Shell

Dominic Breit, Sebastian Schwarzacher

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Abstract

We study the Navier--Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter's elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies γ>12/7 (γ>1 in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in [D. Lengeler, M. Ruzicka, Weak Solutions for an Incompressible Newtonian Fluid Interacting with a Koiter Type Shell. Arch. Ration. Mech. Anal. 211 (2014), no. 1, 205--255] on incompressible Navier--Stokes equations.
Original languageEnglish
Pages (from-to)1-68
Number of pages68
JournalArchive for Rational Mechanics and Analysis
Early online date29 Nov 2017
DOIs
Publication statusE-pub ahead of print - 29 Nov 2017

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