Related papers: Stability of equilibria and bifurcations for a flu…
In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as maximizers of the kinetic energy subject to the constraint…
The equations governing the motion of a three-dimensional liquid drop moving freely in an unbounded liquid reservoir under the influence of a gravitational force are investigated. Provided the (constant) densities in the two liquids are…
Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau--de Gennes equation coupled to an externally-prescribed flow field is the basis for the…
We consider a classical (capillary) model for a one-phase liquid in equilibrium. The liquid (e.g. water) is subject to a volume constraint, it does not mix with the surrounding vapour (e.g. air), it may come into contact with solid supports…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
In this work, we study the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the added-stiffness terms arising in the formulation of Fanion…
We study the dynamics of a mobile impurity in a quantum fluid at zero temperature. Two related settings are considered. In the first setting the impurity is injected in the fluid with some initial velocity ${\mathbf v}_0$, and we are…
In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…
We characterize a system of hard spheres with a simple collision rule that breaks time reversal symmetry, but conserves energy. The collisions lead to an a-chiral, isotropic, and homogeneous stationary state, whose properties are determined…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open…
We consider the interaction of a viscous incompressible fluid with a flexible shell in three space dimensions. The fluid is described by the three-dimensional incompressible Navier--Stokes equations in a domain that is changing in…
We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We…
In this study, we examine the linear stability of an axisymmetric Taylor bubble moving steadily in a flowing liquid enclosed in a circular tube. Linearisation is performed about axisymmetric base states obtained in Part I of this study by…
We study the existence of multiple equilibrium states in a simple fluid network using Newtonian fluids and laminar flow. We demonstrate theoretically the presence of hysteresis and bistability, and we confirm these predictions in an…
We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the…
We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the variation of the undisturbed flow at the body scale is…