相关论文: Migrating elastic flows
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of initial conditions, we classify the homothetically…
A two-layer quasi-geostrophic flow is quite insulated from the surrounding fluid, while the layers interact each other by means of the modulation of the interface between them and of the turbulence affecting the layers in the proximity of…
This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded…
Plane Couette flow of visco-elastic fluids is shown to exhibit a purely elastic subcritical instability in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
In recent years, there has been a growing interest in geometric evolution in heterogeneous media. Here we consider curvature driven fows of planar curves, with an additional space-dependent forcing term. Motivated by a homogenization…
We study the spectral problem associated with the equation governing the small transverse motions of a viscoelastic tube of finite length conveying an ideal fluid. The boundary conditions considered are of general form, accounting for a…
The paper deals with a theoretical study of electrokinetic flow of a rheological Herschel-Bulkley fluid through a cylindrical tube of variable cross-section. The concern of this study is to analyze combined pressure-driven and…
We study the mean curvature flow of graphs both with Neumann boundary conditions and transport terms. We derive boundary gradient estimates for the mean curvature flow. As an application, the existence of the mean curvature flow of graphs…
We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauss curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In…
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…
Elastic confinements play an important role in many soft matter systems and affect the transport properties of suspended particles in viscous flow. On the basis of low-Reynolds-number hydrodynamics, we present an analytical theory of the…
Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors, and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of…
The elastic flow, which is the $L^2$-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are…
In the paper, we consider the solvability of the two-dimensional Navier-Stokes equations in an exterior unit disk. On the boundary of the disk, the tangential velocity is subject to the perturbation of a rotation, and the normal velocity is…
Active liquid crystals or active gels are soft materials which can be physically realised e.g. by preparing a solution of cytoskeletal filaments interacting with molecular motors. We study the hydrodynamics of an active liquid crystal in a…
We study the elastic flow of closed curves and of open curves with clamped boundary conditions in the hyperbolic plane. While global existence and convergence toward critical points for initial data with sufficiently small energy is already…
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…