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arXiv · 1704.06479

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 $γ>\frac{12}{7}$ ($γ>1$ 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.

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Dominic Breit, Sebastian Schwarzacher. 2017-04-21. Compressible fluids interacting with a linear-elastic shell. https://doi.org/10.1007/s00205-017-1199-8

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