TY - JOUR
T1 - Compressible fluids interacting with 3D visco-elastic bulk solids
AU - Breit, Dominic
AU - Kampschulte, Malte
AU - Schwarzacher, Sebastian
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/12
Y1 - 2024/12
N2 - We consider the physical setup of a three-dimensional fluid–structure interaction problem. A viscous compressible gas or liquid interacts with a nonlinear, visco-elastic, three-dimensional bulk solid. The latter is described by an evolution with inertia, a non-linear dissipation term and a term that relates to a non-convex elastic energy functional. The fluid is modelled by the compressible Navier–Stokes equations with a barotropic pressure law. Due to the motion of the solid, the fluid domain is time-changing. Our main result is the long-time existence of a weak solution to the coupled system until the time of a collision. The nonlinear coupling between the motions of the two different matters is established via the method of minimising movements. The motion of both the solid and the fluid is chosen via an incrimental minimization with respect to dissipative and static potentials. These variational choices together with a careful construction of an underlying flow map for our approximation then directly result in the pressure gradient and the material time derivatives.
AB - We consider the physical setup of a three-dimensional fluid–structure interaction problem. A viscous compressible gas or liquid interacts with a nonlinear, visco-elastic, three-dimensional bulk solid. The latter is described by an evolution with inertia, a non-linear dissipation term and a term that relates to a non-convex elastic energy functional. The fluid is modelled by the compressible Navier–Stokes equations with a barotropic pressure law. Due to the motion of the solid, the fluid domain is time-changing. Our main result is the long-time existence of a weak solution to the coupled system until the time of a collision. The nonlinear coupling between the motions of the two different matters is established via the method of minimising movements. The motion of both the solid and the fluid is chosen via an incrimental minimization with respect to dissipative and static potentials. These variational choices together with a careful construction of an underlying flow map for our approximation then directly result in the pressure gradient and the material time derivatives.
KW - 35Q40
KW - 35R35
KW - 76N06
KW - 76N10
UR - http://www.scopus.com/inward/record.url?scp=85192984295&partnerID=8YFLogxK
U2 - 10.1007/s00208-024-02886-w
DO - 10.1007/s00208-024-02886-w
M3 - Article
AN - SCOPUS:85192984295
SN - 0025-5831
VL - 390
SP - 5495
EP - 5552
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 4
ER -