Related papers: On the motion of a viscous liquid filling space
Translation of \'Emile Mathieu's "M\'emoire sur le mouvement vibratoire d'une membrane de forme elliptique", Journal de math\'ematiques pures et appliqu\'ees 2e s\'erie, tome 13 (1868), p. 137-203.
This article offers a modern perspective which exposes the many contributions of Leray in his celebrated work on the Navier--Stokes equations from 1934. Although the importance of his work is widely acknowledged, the precise contents of his…
Recent findings on the displacements in the surroundings of isotropic flow events in viscous liquids [Phys. Rev. E, to appear Feb. 1999] are generalized to the anisotropic case. Also, it is shown that a flow event is characterized by a…
Shear-thinning and viscoelasticity are two non-Newtonian fluid properties widely existing in biological fluids. In this study, we found that the translation motion of a rotating particle near a wall speed up firstly, and then slows down…
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 system "viscous incompressible fluid + rigid body" is assumed to occupy…
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and…
We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk…
We consider the motion of a rigid body immersed in an ideal flow occupying the plane, with bounded initial vorticity. In that case there exists a unique corresponding solution which is global in time, in the spirit of the famous work by…
We study the problem of the motion of the free surface of a compressible fluid. We prove existence for the linearized equations.
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…
This is an English translation of Euler's article "Principia motus fluidorum" in which the Euler equation (in two three dimensions) has been established for the first time in 1752. The actual publication has been delayed by nine years.…
We study the problem of the motion of the free surface of a liquid. We prove existence and stability for the linearized equations.
The physics of liquids in porous media gives rise to many interesting phenomena, including imbibition where a viscous fluid displaces a less viscous one. Here we discuss the theoretical and experimental progress made in recent years in this…
This paper is concerned with the diffusion of a fluid through a viscoelastic solid undergoing large deformations. Using ideas from the classical theory of mixtures and a thermodynamic framework based on the notion of maximization of the…
A body $\mathscr B$ is started from rest by translational motion in an otherwise quiescent Navier-Stokes liquid filling the whole space. We show, for small data, that if after some time $\mathscr B$ reaches a spinless oscillatory motion of…
In a recent Letter (Y. Sumino et al., PRL 94, 068301 (2005)) a spontaneous motion of an oil droplet in the surrounding aqueous media along a glass surface was reported. The authors suggested that the self-locomotion is driven by a…
We correct certain errors and ambiguities in the recent pedagogical article by Hopkins and de Bruyn. The early-time asymptotics of the solution to the transient version of Stokes' second problem for an Oldroyd-B fluid in a half-space is…
Chaplygin's equations describing the planar motion of a rigid body in an unbounded volume of an ideal fluid involved in a circular flow around the body are considered. Hamiltonian structures, new integrable cases, and partial solutions are…
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On the geodesic diameter of surfaces with involutive isometry (Russian), Tr. Rubtsovsk. Ind. Inst., 2001, V. 9, 62-65, Zbl. 1015.53041. All…
The motion of colloids in the flow field of a viscous liquid is investigated. The small colloid size compare to the macroscopical scale of the flow allow to calculate their velocity relative to that of the liquid. If the inner colloid…