共查询到20条相似文献,搜索用时 15 毫秒
1.
Takayuki Kobayashi Takashi Suzuki Kazuo Watanabe 《Journal of Mathematical Fluid Mechanics》2006,8(3):382-397
This paper is concerned with the component-wise regularity of the solution to the stationary Maxwell or Stokes systems. We
assume that there is a surface
in R3, regarded as an interface, and the solution u to one of the systems is smooth except for this
. Then, under these assumptions, we can show that some components of u are smooth across
. In the Maxwell system, the normal component of u is always regular across
. On the other hand, in the Stokes system, the singularity of u across
can only arise to the normal derivatives of its tangential components. Furthermore, these results are shown to be optimal. 相似文献
2.
We consider here a model of fluid-structure evolution
problem which, in particular, has been largely studied from the
numerical point of view. We prove the existence of a strong
solution to this problem. 相似文献
3.
The steady state system of isothermal Navier–Stokes equations is considered in two dimensional domain including an obstacle.
The shape optimisation problem of minimisation of the drag with respect to the admissible shape of the obstacle is defined.
The generalized solutions for the Navier–Stokes equations are introduced. The existence of an optimal shape is proved in the
class of admissible domains. In general the solutions are not unique for the problem under considerations. 相似文献
4.
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
5.
Ivan V. Basov 《Journal of Mathematical Fluid Mechanics》2005,7(4):515-528
A compressible one-dimensional plain Bingham flow starting in equilibrium under the action of a time-increasing spatially
homogeneous mass force is investigated. A lower estimate for the width of a rigid zone is obtained. The estimate shows that
the rigid zone converges to the whole interval for t tends to zero. In other words, existence of a rigid core is established.
As a supplementary result, additional smoothness of solutions to the system considered is established. 相似文献
6.
In this paper, we consider weak solutions to the equations of stationary motion of a class of non-Newtonian fluids the constitutive law of which includes the power law model as special case. We prove the existence of second order derivatives of weak solutions to these equations. 相似文献
7.
We obtain local estimates of the steady-state Stokes system
without pressure near boundary.
As an application of the local estimates, we prove the partial regularity
up to the boundary for the stationary Navier-Stokes equations
in a smooth domain in five dimension. 相似文献
8.
Antonin Chambolle Benoît Desjardins Maria J. Esteban Céline Grandmont 《Journal of Mathematical Fluid Mechanics》2005,7(3):368-404
The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane. 相似文献
9.
Muriel Boulakia 《Journal of Mathematical Fluid Mechanics》2007,9(2):262-294
We study here the three-dimensional motion of an elastic structure immersed in an incompressible viscous fluid. The structure
and the fluid are contained in a fixed bounded connected set Ω. We show the existence of a weak solution for regularized elastic
deformations as long as elastic deformations are not too important (in order to avoid interpenetration and preserve orientation
on the structure) and no collisions between the structure and the boundary occur. As the structure moves freely in the fluid,
it seems natural (and it corresponds to many physical applications) to consider that its rigid motion (translation and rotation)
may be large.
The existence result presented here has been announced in [4]. Some improvements have been provided on the model: the model
considered in [4] is a simplified model where the structure motion is modelled by decoupled and linear equations for the translation,
the rotation and the purely elastic displacement. In what follows, we consider on the structure a model which represents the
motion of a structure with large rigid displacements and small elastic perturbations. This model, introduced by [15] for a
structure alone, leads to coupled and nonlinear equations for the translation, the rotation and the elastic displacement. 相似文献
10.
Zdeněk Skalák 《Journal of Mathematical Fluid Mechanics》2007,9(4):565-587
In the paper we study the asymptotic dynamics of strong global solutions of the Navier Stokes equations. We are concerned
with the question whether or not a strong global solution w can pass through arbitrarily large fast decays. Avoiding results on higher regularity of w used in other papers we prove as the main result that for the case of homogeneous Navier–Stokes equations the answer is negative:
If [0, 1/4) and δ0 > 0, then the quotient remains bounded for all t ≥ 0 and δ∈[0, δ0]. This result is not valid for the non-homogeneous case. We present an example of a strong global solution w of the non-homogeneous Navier–Stokes equations, where the exterior force f decreases very quickly to zero for while w passes infinitely often through stages of arbitrarily large fast decays. Nevertheless, we show that for the non-homogeneous
case arbitrarily large fast decays (measured in the norm cannot occur at the time t in which the norm is greater than a given positive number.
相似文献
11.
We investigate the steady compressible Navier–Stokes system of equations in the isentropic regime in a domain with several
conical outlets and with prescribed pressure drops. Existence of weak solutions is proved and estimate of these solutions
with respect to the pressure drops is derived under the hypothesis γ > 3 where γ is the adiabatic constant. 相似文献
12.
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
13.
Hiroko Morimoto 《Journal of Mathematical Fluid Mechanics》2007,9(3):411-418
Let Ω be a 2-dimensional bounded domain, symmetric with respect to the x2-axis. The boundary has several connected components, intersecting the x2-axis. The boundary value is symmetric with respect to the x2-axis satisfying the general outflow condition. The existence of the symmetric solution to the steady Navier–Stokes equations
was established by Amick [2] and Fujita [4]. Fujita [4] proved a key lemma concerning the solenoidal extension of the boundary
value by virtual drain method. In this note, we give a different proof via elementary approach by means of the stream function. 相似文献
14.
Yasunori Maekawa 《Journal of Mathematical Fluid Mechanics》2008,10(1):89-105
In this paper we establish spatial decay estimates for derivatives of vorticities solving the two-dimensional vorticity equations
equivalent to the Navier–Stokes equations. As an application we derive asymptotic behaviors of derivatives of vorticities
at time infinity. It is well known by now that the vorticity behaves asymptotically as the Oseen vortex provided that the
initial vorticity is integrable. We show that each derivative of the vorticity also behaves asymptotically as that of the
Oseen vortex.
相似文献
15.
We study the boundary-value problem associated with the Oseen system in the exterior of m Lipschitz domains of an euclidean point space
We show, among other things, that there are two positive constants
and α depending on the Lipschitz character of Ω such that: (i) if the boundary datum a belongs to Lq(∂Ω), with q ∈ [2,+∞), then there exists a solution (u, p), with
and u ∈ L∞(Ω) if a ∈ L∞(∂Ω), expressed by a simple layer potential plus a linear combination of regular explicit functions; as a consequence, u tends nontangentially to a almost everywhere on ∂Ω; (ii) if a ∈ W1-1/q,q(∂Ω), with
then ∇u, p ∈ Lq(Ω) and if a ∈ C0,μ(∂Ω), with μ ∈ [0, α), then
also, natural estimates holds. 相似文献
16.
17.
David Hoff 《Journal of Mathematical Fluid Mechanics》2005,7(3):315-338
We prove the global existence of weak solutions of the Navier–Stokes equations of compressible flow in a half-space with the boundary condition proposed by Navier: the velocity on the boundary is proportional to the tangential component of the stress. This boundary condition allows for the determination of the scalar function in the Helmholtz decomposition of the acceleration density, which in turn is crucial in obtaining pointwise bounds for the density. Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. These results generalize previous results for solutions in the whole space and are the first for solutions in this intermediate regularity class in a region with a boundary. 相似文献
18.
We consider the Cauchy problem for incompressible Navier–Stokes equations
with initial data in
, and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have
, as long as
stays finite. 相似文献
19.
Michael Struwe 《Journal of Mathematical Fluid Mechanics》2007,9(2):235-242
We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result
of Zhou [28]. 相似文献
20.
Burgers vortices are stationary solutions of the three-dimensional Navier–Stokes equations in the presence of a background
straining flow. These solutions are given by explicit formulas only when the strain is axisymmetric. In this paper we consider
a weakly asymmetric strain and prove in that case that non-axisymmetric vortices exist for all values of the Reynolds number.
In the limit of large Reynolds numbers, we recover the asymptotic results of Moffatt, Kida & Ohkitani [11]. We also show that
the asymmetric vortices are stable with respect to localized two-dimensional perturbations. 相似文献