Related papers: Unrestricted deformations of thin elastic structur…
We address semigroup well-posedness for a linear, compressible viscous fluid interacting at its boundary with an elastic plate. We derive the model by linearizing the compressible Navier-Stokes equations about an arbitrary flow state, so…
In this paper, we investigate the dynamics of an incompressible viscous Navier-Stokes fluid evolving above a one-dimensional flat surface. The fluid is subject to a uniform gravitational field and capillary forces acting along the free…
The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence and heat transport modification in natural convection, and is one…
In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance…
The motion of an elastic solid inside of 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…
We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in…
Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points,…
We study a 3D nonlinear moving boundary fluid-structure interaction problem describing the interaction of the fluid flow with a rigid body. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the…
We investigate the equilibrium of a fluid in contact with a solid boundary through a density-functional theory. Depending on the conditions, the fluid can be in one phase, gas or liquid, or two phases, while the wall induces an external…
The dynamic of contact formation between soft materials immersed in a fluid is accompanied by fluid drainage and elastic deformation. As a result, controlling the coupling between lubrication pressure and elasticity provides strategies to…
We study a coupled fluid-structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier--Stokes equations in a 2D rectangular type domain where the upper part of the domain is described…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body's boundary. The whole `viscous incompressible fluid + rigid body' system is assumed to occupy…
We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary…
A problem on propagation of waves in deformable shells with flowing liquid is very urgent in connection with wide use of liquid transportation systems in living organisms and technology. It is necessary to consider shell motion equations…
We study the local controllability properties of 2D and 3D bio-mimetic swimmers employing the change of their geometric shape to propel themselves in an incompressible fluid described by Navier-Stokes equations. It is assumed that swimmers'…
We consider a system of multiple insulating rigid bodies moving inside of an electrically conducting compressible fluid. In this system we take into account the interaction of the fluid with the bodies as well as with the electromagnetic…
Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a…