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 $\gamma >\frac{12}{7}$ ($\gamma >1$ in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in [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.

References in corpus (4)

• On the motion of an elastic solid inside of an incompressible viscous fluid
• On the interaction between quasilinear elastodynamics and the Navier-Stokes equations
• Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls
• Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains

Cited by in corpus (9)

• Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation
• A Time Domain Approach for the Exponential Stability of a Nondissipative Linearized Compressible Flow-Structure PDE System
• On a fluid-structure interaction problem for plaque growth: cylindrical domain
• An incompressible polymer fluid interacting with a Koiter shell
• Construction of a right inverse for the divergence in non-cylindrical time dependent domains
• Short time existence of a quasi-stationary fluid-structure interaction problem for plaque growth
• On a diffuse interface model for incompressible viscoelastic two-phase flows
• Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling
• Weak solutions and singular limits for a compressible fluid-structure interaction problem with slip boundary conditions