# Compressible Fluids Interacting with a Linear-Elastic Shell

Compressible Fluids Interacting with a Linear-Elastic Shell 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 $${\gamma > \frac{12}{7}}$$ γ > 12 7 ( $${\gamma >1 }$$ 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 Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205–255, 2014) on incompressible Navier–Stokes equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

# Compressible Fluids Interacting with a Linear-Elastic Shell

, Volume 228 (2) – Nov 29, 2017
68 pages

/lp/springer_journal/compressible-fluids-interacting-with-a-linear-elastic-shell-68gXBLC0mN
Publisher
Springer Journals
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-017-1199-8
Publisher site
See Article on Publisher Site

### 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 $${\gamma > \frac{12}{7}}$$ γ > 12 7 ( $${\gamma >1 }$$ 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 Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205–255, 2014) on incompressible Navier–Stokes equations.

### Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Nov 29, 2017

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