共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
In this paper we take up the question of analyticity properties of Dirichlet–Neumann operators (DNO) which arise in boundary
value and free boundary problems from a wide variety of applications (e.g., fluid and solid mechanics, electromagnetic and
acoustic scattering). More specifically, we consider DNO defined on domains inspired by the simulation of ocean waves over
bathymetry, i.e. domains perturbed independently at both the top and bottom. Our analysis shows that the DNO, when perturbed
from an arbitrary smooth domain, is parametrically analytic (as a function of deformation height/slope) for profiles of finite
smoothness. Additionally, we extend these results to joint spatial and parametric analyticity when the perturbations are real
analytic. This analysis is novel not only in that it accounts for the doubly perturbed nature of the geometry, but also in
that the technique of proof establishes the full joint analyticity from an arbitrary smooth profile simultaneously.
相似文献
4.
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
5.
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
6.
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
7.
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
8.
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
9.
T. Roubíček 《Journal of Mathematical Fluid Mechanics》2009,11(1):110-125
The model combining incompressible Navier–Stokes’ equation in a non-Newtonian p-power-law modification and the nonlinear heat equation is considered. Existence of its (very) weak solutions is proved for
p > 11/5 under mild assumptions of the temperature-dependent stress tensor by careful successive limit passage in a Galerkin
approximation.
相似文献
10.
11.
We consider the asymptotic limit for the complete Navier–Stokes–Fourier system as both Mach and Froude numbers tend to zero.
The limit is investigated in the context of weak variational solutions on an arbitrary large time interval and for the ill-prepared
initial data. The convergence to the Oberbeck–Boussinesq system is shown.
相似文献
12.
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
13.
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
14.
Jiří Neustupa 《Journal of Mathematical Fluid Mechanics》2009,11(1):22-45
We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain
Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by
the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured
in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.
相似文献
15.
This paper is devoted to a scalar model of the Oseen equations, a linearized form of the Navier–Stokes equations. To control
the behavior of functions at infinity, the problem is set in weighted Sobolev spaces including anisotropic weights. In a first
step, some weighted Poincaré-type inequalities are obtained. In a second step, we establish existence, uniqueness and regularity
results. 相似文献
16.
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
17.
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
18.
In this paper we solve the stationary Oseen equations in
. The behavior of the solutions at infinity is described by setting the problem in weighted Sobolev spaces including anisotropic
weights. The study is based on a Lp theory for 1 < p < ∞. 相似文献
19.
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
20.
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