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.
Highlights
IntroductionFluid structure interactions have been studied intensively by engineers, physicists and mathematicians
Fluid structure interactions have been studied intensively by engineers, physicists and mathematicians. This is motivated by a plethora of applications anytime a fluid force is balanced by some flexible material; for instance in hydro- and aero-elasticity [7,16] or biomechanics [4]
In this work we consider the motion of an isentropic compressible fluid in a three-dimensional body
Summary
Fluid structure interactions have been studied intensively by engineers, physicists and mathematicians. This is motivated by a plethora of applications anytime a fluid force is balanced by some flexible material; for instance in hydro- and aero-elasticity [7,16] or biomechanics [4]. The displacement of the boundary is prescribed via a two dimensional surface representing a Kirchhof– Love shell. We prove the existence of a weak solution to the coupled compressible Navier–Stokes system interacting with the Kirchhof– Love shell on a part of the boundary. The time interval of existence is only restricted once a self-intersection of the moving boundary (namely the shell) is approached
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