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Compressible Fluids Interacting with a Linear-Elastic Shell

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 \({\gamma > \frac{12}{7}}\) (\({\gamma >1 }\) in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205–255, 2014) on incompressible Navier–Stokes equations.

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Correspondence to Dominic Breit.

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Communicated by P. Constantin

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Breit, D., Schwarzacher, S. Compressible Fluids Interacting with a Linear-Elastic Shell. Arch Rational Mech Anal 228, 495–562 (2018). https://doi.org/10.1007/s00205-017-1199-8

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