Compressible Fluids Interacting with a Linear-Elastic Shell

Abstrakt

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 > 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 Ruzicka (Arch Ration Mech Anal 211(1):205-255, 2014) on incompressible Navier-Stokes equations.

Klíčová slova

• navier-stokes equations
• koiter type shell
• weak solutions
• viscous-fluid
• unsteady interaction
• existence
• domains
• system
• energy
• motion