共查询到20条相似文献,搜索用时 15 毫秒
1.
Dorin Bucur Eduard Feireisl Šárka Nečasová 《Journal of Mathematical Fluid Mechanics》2008,10(4):554-568
We consider a stationary Navier–Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming
the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional
to a small parameter ε, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system
of the Navier–Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary
conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is
allowed without any constraint.
The work of Š. N. supported by Grant IAA100190505 of GA ASCR in the framework of the general research programme of the Academy
of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503. 相似文献
2.
In this article the global solvability of the initial-boundary value problems for the system of equations describing non-stationary
flow of the viscous heat-conducting one-dimensional gas in time-decreasing non-rectangular domains is proved.
相似文献
3.
Michael Sever 《Journal of Mathematical Fluid Mechanics》2008,10(2):203-223
Lack of hyperbolicity is a recurring problem for models of two-phase flow assuming the form of systems of balance laws. In
particular, smooth solutions occur only for very special initial data, and the standard results on the local structure of
discontinuous weak solutions do not apply to such nonhyperbolic systems. A simple example is inviscid, incompressible two-fluid
flow with a single pressure.
We suggest that such an unattractive mathematical feature may result from the mathematical derivation of the model, rather
than from the underlying physical assumptions. In particular, for the case described above we present an alternative treatment
which leads to a consistent model for piecewise smooth, discontinuous solutions. We obtain admissibility conditions for the
anticipated discontinuities by considering the limit of vanishing viscosity with a convenient dissipation term.
相似文献
4.
Hyeong-Ohk Bae 《Journal of Mathematical Fluid Mechanics》2008,10(4):503-530
We estimate the time decay rates in L
1, in the Hardy space and in L
∞ of the gradient of solutions for the Stokes equations on the half spaces. For the estimates in the Hardy space we adopt the
ideas in [7], and also use the heat kernel and the solution formula for the Stokes equations.
We also estimate the temporal-spatial asymptotic estimates in L
q
, 1 < q < ∞, for the Stokes solutions.
This work was supported by grant No. (R05-2002-000-00002-0(2002)) from the Basic Research Program of the Korea Science & Engineering
Foundation. 相似文献
5.
Luigi C. Berselli 《Journal of Mathematical Fluid Mechanics》2009,11(2):171-185
In this paper we improve the results stated in Reference [2], in this same Journal, by using -basically- the same tools. We
consider a non Newtonian fluid governed by equations with p-structure and we show that second order derivatives of the velocity and first order derivatives of the pressure belong to
suitable Lebesgue spaces.
相似文献
6.
Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional
Navier–Stokes equations on a sphere. The stationary flow on the sphere has two singularities (a sink and a source) at the
North and South poles of the sphere. We prove analytically for the linearized Navier–Stokes equations that the stationary
flow is asymptotically stable. When the spherical layer is truncated between two symmetrical rings, we study eigenvalues of
the linearized equations numerically by using power series solutions and show that the stationary flow remains asymptotically
stable for all Reynolds numbers.
相似文献
7.
Didier Bresch El Hassan Essoufi Mamadou Sy 《Journal of Mathematical Fluid Mechanics》2007,9(3):377-397
In this paper, we look at the influence of the choice of the Reynolds tensor on the derivation of some multiphasic incompressible
fluid models, called Kazhikhov–Smagulov type models. We show that a compatibility condition between the viscous tensor and
the diffusive term allows us to obtain similar models without assuming a small diffusive term as it was done for instance
by A. Kazhikhov and Sh. Smagulov. We begin with two examples: The first one concerning pollution and the last one concerning
a model of combustion at low Mach number. We give the compatibility condition that provides a class of models of the Kazhikhov–Smagulov
type. We prove that these models are globally well posed without assumptions between the density and the diffusion terms. 相似文献
8.
9.
Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists T
0 > 0, ν
0 > 0 and a unique continuous family of strong solutions u
ν
(0 ≤ ν < ν
0) of the Euler or Navier–Stokes initial-boundary value problem on the time interval (0, T
0). In addition to the condition of the zero flux, the solutions of the Navier–Stokes equation satisfy certain natural boundary
conditions imposed on curl
u
ν
and curl
2
u
ν
.
相似文献
10.
H. Beirão da Veiga 《Journal of Mathematical Fluid Mechanics》2009,11(2):233-257
In this article we prove some sharp regularity results for the stationary and the evolution Navier–Stokes equations with shear
dependent viscosity, see (1.1), under the no-slip boundary condition(1.4). We are interested in regularity results for the
second order derivatives of the velocity and for the first order derivatives of the pressure up to the boundary, in dimension n ≥ 3. In reference [4] we consider the stationary problem in the half space
\mathbbR+n{\mathbb{R}}_+^n under slip and no-slip boundary conditions. Here, by working in a simpler context, we concentrate on the basic ideas of proofs.
We consider a cubic domain and impose our boundary condition (1.4) only on two opposite faces. On the other faces we assume
periodicity, as a device to avoid unessential technical difficulties. This choice is made so that we work in a bounded domain
Ω and, at the same time, with a flat boundary. In the last section we provide the extension of the results from the stationary
to the evolution problem. 相似文献
11.
Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability
estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As an application, we construct approximations
for the time-dependent Stokes equations with a source term in L
p
(0, T; L
q
(Ω)) and prove uniform estimates on the time derivative and discrete Laplacian of the discrete velocity that are similar to
those in Sohr and von Wahl [20].
On long leave from LIMSI (CNRS-UPR 3251), BP 133, 91403, Orsay, France. 相似文献
12.
Michael Renardy 《Journal of Mathematical Fluid Mechanics》2009,11(1):91-99
We prove the global existence in time of solutions to time-dependent shear flows for certain viscoelastic fluids. The essential
point in the proof is an a priori estimate for the shear stress. Positive definiteness constraints for the stress play a crucial
role in obtaining such estimates.
This research was supported by the National Science Foundation under Grant DMS-0405810. 相似文献
13.
Michael Renardy 《Journal of Mathematical Fluid Mechanics》2009,11(1):100-109
We consider plane shear flows of viscoelastic fluids. For a number of constitutive models, we prove stability of the rest
state for perturbations of arbitrary size. We also consider stability of plane Poiseuille flow in a few special cases.
This research was supported by the National Science Foundation under Grant DMS-0405810. 相似文献
14.
K. Pileckas 《Journal of Mathematical Fluid Mechanics》2006,8(4):542-563
The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite
cylinder is proved. We assume that the initial data and the external forces do not depend on x3 and find the solution (u, p) having the following form
where x′ = (x1, x2). Such solution generalize the nonstationary Poiseuille solutions. 相似文献
15.
Konstantin Pileckas 《Journal of Mathematical Fluid Mechanics》2008,10(2):272-309
The time-dependent Navier–Stokes system is studied in a two-dimensional domain with strip-like outlets to infinity in weighted
Sobolev function spaces. It is proved that under natural compatibility conditions there exists a unique solution with prescribed
fluxes over cross-sections of outlets to infinity which tends in each outlet to the corresponding time-dependent Poiseuille
flow. The obtained results are proved for arbitrary large norms of the data (in particular, for arbitrary fluxes) and globally
in time.
The authors are supported by EC FP6 MC–ToK programme SPADE2, MTKD–CT–2004–014508. 相似文献
16.
We consider asymptotic behavior of Leray’s solution which expresses axis-symmetric incompressible Navier–Stokes flow past
an axis-symmetric body. When the velocity at infinity is prescribed to be nonzero constant, Leray’s solution is known to have
optimum decay rate, which is in the class of physically reasonable solution. When the velocity at infinity is prescribed to
be zero, the decay rate at infinity has been shown under certain restrictions such as smallness on the data. Here we find
an explicit decay rate when the flow is axis-symmetric by decoupling the axial velocity and the horizontal velocities.
The first author was supported by KRF-2006-312-C00466. The second author was supported by KRF-2006-531-C00009. 相似文献
17.
Darya Apushkinskaya Michael Bildhauer Martin Fuchs 《Journal of Mathematical Fluid Mechanics》2005,7(2):261-297
We consider the stationary flow of a generalized Newtonian fluid which is modelled by an anisotropic dissipative potential f. More precisely, we are looking for a solution
of the following system of nonlinear partial differential equations
Here
denotes the pressure, g is a system of volume forces, and the tensor T is the gradient of the potential f. Our main hypothesis imposed on f is the existence of exponents 1 < p q0 < such that
holds with constants , > 0. Under natural assumptions on p and q0 we prove the existence of a weak solution u to the problem (*), moreover we prove interior C1,-regularity of u in the two-dimensional case. If n = 3, then interior partial regularity is established. 相似文献
((*)) |
18.
Natalia Strong 《Journal of Mathematical Fluid Mechanics》2008,10(4):488-502
The present paper examines the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal
layer of fluid saturating a porous medium. A constant temperature distribution is assigned on the rigid boundaries, so that
there exists a vertical temperature gradient. The mathematical model is described by equations of filtration convection in
the Darcy–Oberbeck–Boussinesq approximation. The linear stability analysis for the quasi-equilibrium solution is performed
using Floquet theory. Employment of the method of continued fractions allows derivation of the dispersion equation for the
Floquet exponent σ in an explicit form. The neutral curves of the Rayleigh number Ra versus horizontal wave number α for the
synchronous and subharmonic resonant modes are constructed for different values of frequency Ω and amplitude A of vibration. Asymptotic formulas for these curves are derived for large values of Ω using the method of averaging, and,
for small values of Ω, using the WKB method. It is shown that, at some finite frequencies of vibration, there exist regions
of parametric instability. Investigations carried out in the paper demonstrate that, depending on the governing parameters
of the problem, vertical vibration can significantly affect the stability of the system by increasing or decreasing its susceptibility
to convection.
相似文献
19.
Adrian Constantin Rossen I. Ivanov Emil M. Prodanov 《Journal of Mathematical Fluid Mechanics》2008,10(2):224-237
We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian
structure, which becomes Hamiltonian for steady waves.
相似文献
20.
Xinyu He 《Journal of Mathematical Fluid Mechanics》2007,9(3):398-410
Let
be the exterior of the closed unit ball. Consider the self-similar Euler system
Setting α = β = 1/2 gives the limiting case of Leray’s self-similar Navier–Stokes equations. Assuming smoothness and smallness of the boundary
data on ∂Ω, we prove that this system has a unique solution
, vanishing at infinity, precisely
The self-similarity transformation is v(x, t) = u(y)/(t* − t)α, y = x/(t* − t)β, where v(x, t) is a solution to the Euler equations. The existence of smooth function u(y) implies that the solution v(x, t) blows up at (x*, t*), x* = 0, t* < + ∞. This isolated singularity has bounded energy with unbounded L
2 − norm of curl v. 相似文献