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 ( 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.
Cite
@article{arxiv.1704.06479,
title = {Compressible fluids interacting with a linear-elastic shell},
author = {Dominic Breit and Sebastian Schwarzacher},
journal= {arXiv preprint arXiv:1704.06479},
year = {2018}
}