Motion of an Elastic Solid inside an Incompressible Viscous Fluid

Motion of an Elastic Solid inside an Incompressible Viscous Fluid

The motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of regularity which has left the basic question of existence open until now. In this paper, we prove the existence and uniqueness of such motions (locally in time), whe...

Mathematical models of turbulent motion of an incompressible viscous fluid

Incompressible fluid inside an astrophysical black hole ?

It is argued that under natural hypothesis the Fermions inside a black hole formed after the collapse of a neutron star could form a non compressible fluid (well before reaching the Planck scale) leading to some features of integer Quantum Hall Effect. The relations with black hole entropy are analyzed. Insights coming from Quantum Hall Effect are used to analyze the coupling with Einstein equa...

Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid

We analyze the influence of pre-stress on the propagation of interfacial waves along the boundary of an incompressible hyperelastic half-space that is in contact with a viscous fluid extending to infinity in the adjoining half-space. One aim is to derive rigorously the incremental boundary conditions at the interface; this derivation is delicate because of the interplay between the Lagrangian a...

Fluid-structure interaction between an incompressible, viscous 3D fluid and an elastic shell with nonlinear Koiter membrane energy

The long-time existence of a weak solution is proved for a nonlinear, fluid-structure interaction (FSI) problem between an incompressible, viscous fluid and a semilinear cylindrical Koiter membrane shell with inertia. No axial symmetry is assumed in the problem. The fluid flow is driven by the timedependent dynamic pressure data prescribed at the inlet and outlet boundaries of the 3D cylindrica...