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1.
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), when the elastic solid is the linear Kirchhoff elastic material. The solution is found using a topological fixed-point theorem that requires the analysis of a linear problem consisting of the coupling between the time-dependent Navier-Stokes equations set in Lagrangian variables and the linear equations of elastodynamics, for which we prove the existence of a unique weak solution. We then establish the regularity of the weak solution; this regularity is obtained in function spaces that scale in a hyperbolic fashion in both the fluid and solid phases. Our functional framework is optimal, and provides the a priori estimates necessary for us to employ our fixed-point procedure.This revised version was published in April 2005. The volume number has now been inserted into the citation line. 相似文献
2.
V. M. Shapovalov S. V. Lapshina 《Journal of Applied Mechanics and Technical Physics》2004,45(1):45-53
Equations of spatial motion of a curved finitelength rod in a viscous fluid flow are derived. Analytical solutions of problems on the motion of a straight rod under conditions of pure shear, simple shear, and uniaxial extension of the fluid are obtained. Longitudinal stability of the straight rod during its spatial motion is considered. Effective viscosity of a suspension filled by rigid straight rods is evaluated. 相似文献
3.
G. Ya. Dynnikova 《Fluid Dynamics》2003,38(5):670-678
The diffusion and annihilation of vortices in axisymmetric and plane incompressible viscous fluid flows are considered. A formula relating the pressure with the velocity of the vortices in the viscous fluid is obtained. 相似文献
4.
V. L. Sennitskii 《Journal of Applied Mechanics and Technical Physics》2001,42(1):72-76
The motion of a rigid sphere in a viscous fluid due to specified pulsations of the sphere and specified oscillations of the fluid away from the sphere is considered. 相似文献
5.
Eduard Feireisl 《Archive for Rational Mechanics and Analysis》2003,167(4):281-308
We prove the existence of global-in-time weak solutions to a model describing the motion of several rigid bodies in a viscous
compressible fluid. Unlike most recent results of similar type, there is no restriction on the existence time, regardless
of possible collisions of two or more rigid bodies and/or a contact of the bodies with the boundary.
(Accepted September 23, 2002)
Published online February 4, 2003
Communicated by Y. Brenier 相似文献
6.
. We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of with Dirichlet boundary conditions. By introducing an appropriate weak formulation for the complete problem, we prove existence
of solutions for initial velocities in . In the absence of collisions, solutions exist for all time in dimension 2, whereas in dimension 3 the lifespan of solutions
is infinite only for small enough data.
(Accepted June 10, 1998) 相似文献
7.
8.
Analytical solutions are obtained for two problems of transverse internal waves in a viscous fluid contacting with a flat layer of a fixed porous medium. In the first problem, the waves are considered which are caused by the motion of an infinite flat plate located on the fluid surface and performing harmonic oscillations in its plane. In the second problem, the waves are caused by periodic shear stresses applied to the free surface of the fluid. To describe the fluid motion in the porous medium, the unsteady Brinkman equation is used, and the motion of the fluid outside the porous medium is described by the Navier–Stokes equation. Examples of numerical calculations of the fluid velocity and filtration velocity profiles are presented. The existence of fluid layers with counter-directed velocities is revealed. 相似文献
9.
In this paper, we consider a two-dimensional fluid-rigid body problem.
The motion of the fluid is modelled by the Navier-Stokes equations, whereas
the dynamics of the rigid body is governed by the conservation
laws of linear and angular momentum. The rigid body is supposed
to be an infinite cylinder of circular cross-section.
Our main result is the existence and uniqueness of global strong solutions. 相似文献
10.
11.
A. N. Prokunin 《Fluid Dynamics》2003,38(3):443-457
The results of an experimental investigation of spherical particles with different surface roughnesses rolling under their own weight down an inclined pipe wall in a Newtonian fluid at low Reynolds numbers, both with (friction should be taken into account) and without contact with the wall, are presented. It is shown that a fixed particle moves differently in different fluids with similar viscosities and densities. This fact, as well as the possibility of particle motion without contact with the wall, cannot be explained within the framework of the usual hydrodynamic theories. An example is the dependence of the particle motion on the static pressure. 相似文献
12.
V. M. Shapovalov S. V. Lapshina 《Journal of Applied Mechanics and Technical Physics》2003,44(2):198-203
The equations of the dynamics of a finitelength curved rod in a viscous flow are derived. The longitudinal stability of the rod against small deflections from a rectilinear form is studied for two types of flow (pure and simple shear). The minimum flexural rigidity of the rod that ensures rod stability for any orientation in the flow is found. The effective viscosity of a suspension filled with rectilinear discrete fibers is estimated. 相似文献
13.
14.
International Applied Mechanics - The motion of a solid body with a cavity containing a heavy multilayer ideal incompressible fluid is considered using a linear problem statement. An algorithm for... 相似文献
15.
V. A. Babkin 《Fluid Dynamics》2002,37(4):587-593
Exact solutions are obtained for the following three problems in which the Brinkman filtration equations are used: laminar fluid flow between parallel plane walls, one of which is rigid while the other is a plane layer of saturated porous medium, motion of a plane porous layer between parallel layers of viscous fluid, and laminar fluid flow in a cylindrical channel bounded by an annular porous layer. 相似文献
16.
E. A. BABKIN V. A. BRAILOVSKAYA D. CLAMOND PH. FRAUNIE YU. A. STEPANYANTS 《International Journal of Computational Fluid Dynamics》2013,27(2):185-202
Evolution of the vortices of monopole and dipole types in a viscous fluid is considered numerically. Theory and numerical results are compared for some particular exact solutions. A good agreement is obtained for the dipole vortices (viscous Chaplygin-Lamb vortices) moving with variable velocities due to viscosity. For the monopole type vortices, the agreement is more or less good only at an initial stage of their evolution; while in the long-lime asymptotics the law of vorticity decay other than the theoretical one is discovered. The reason for such a discrepancy is discussed. The interactions of dipole vortices with each other and with rigid boundaries are studied too. The stability of dipole vortices with complex internal structures is considered briefly. 相似文献
17.
Sébastien Court 《Journal of Dynamics and Differential Equations》2017,29(2):737-782
We study a coupled system modeling the movement of a deformable solid inside a viscous incompressible fluid. For the solid we consider a given deformation which has to obey several physical constraints. The motion of the fluid is modeled by the incompressible Navier–Stokes equations in a time-dependent bounded domain of \(\mathbb {R}^3\), and the solid satisfies the Newton’s laws. Our contribution consists in adapting and completing in dimension 3, some existing results, in a framework where the regularity of the deformation of the solid is limited. We rewrite the main system in domains which do not depend on time, by using a new means of defining a change of variables, and a suitable change of unknowns. We study the corresponding linearized system before setting a local-in-time existence result. Global existence is obtained for small data, and in particular for deformations of the solid which are close to the identity. 相似文献
18.
E. N. Cheremnykh 《Journal of Applied Mechanics and Technical Physics》2018,59(3):416-421
This paper touches upon an initial-boundary-value problem that describes the unidirectional heat-gravitational motion of fluid in a plane channel in the case of solid immobile upper and lower walls with temperature distribution thereon and in the case of a heat-insulated upper wall. The motion is caused by a joint effect of the longitudinal temperature gradient and given nonstationary flow rate. The initial-boundary-value problem is inverse relative to the pressure gradient along the channel. An exact stationary solution is obtained. A solution of the nonstationary problems in Laplace images is determined, and the results of numerical calculations are presented. 相似文献
19.
本文给出了流固偶合运动(包括物体散射辐射及偶合运动)的边界元法理论和应用.对于散射问题,求出了物体引起的散射势及入射波作用于物体的载荷.对于辐射问题,求出了辐射势及物体在流体中运动的附加质量和附加阻尼.偶合问题包括求其中包含的散射势和辐射势以及作用于物体之上的散射力、物体的附加质量、附加阻尼、物体在入射波作用下的运动.在偶合运动问题中,本文采取了边界积分方程与物体在流体中的运动方程联立求解的方法,并将其运用到边界元法的数值过程中.所编制的程序有较高的精度.最后给出了数值计算结果与理论解的比较. 相似文献
20.
In this paper, we are concerned with free boundary problem for
compressible viscous isotropic Newtonian fluid.
Our problem is to find the three-dimensional domain occupied by
the fluid which is bounded below by the fixed bottom and above
by the free surface together with the density, the velocity
vector field and the absolute temperature of the fluid
satisfying the system of Navier-Stokes equations and the
initial-boundary conditions.
The Navier-Stokes equations consist of the conservations of
mass, momentum under the gravitational field in a downward
direction and energy.
The effect of the surface tension on the free surface is taken
into account.
The purpose of this paper is to establish two existence theorems
to the problem mentioned above: the first concerns with the
temporary local solvability in anisotropic
Sobolev-Slobodetskiĭ spaces and the second the global
solvability near the equilibrium rest state.
Here the equilibrium rest state (heat conductive state) means
that the temperature distribution is a linear function with
respect to a vertical direction and the density is determined by
an ordinary differential equation which involves equation of
state. For the proof, we rely on the methods due to Solonnikov in the
case of incompressible fluid with some modifications, since our
problem is hyperbolic-parabolic coupled system.
Dedicated to Professors Takaaki Nishida and Masayasu Mimura on their sixtieth birthdays 相似文献