Year: 2017
Type: article
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.
Authors: Dominic Breit, Sebastian Schwarzacher
Institutions: Heriot-Watt University, Charles University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W2963198323