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1.
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
2.
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
3.
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
4.
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
5.
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
6.
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.
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7.
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
8.
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
9.
Hisashi Okamoto 《Journal of Mathematical Fluid Mechanics》2009,11(1):46-59
The generalized Proudman–Johnson equation, which was derived from the Navier–Stokes equations by Jinghui Zhu and the author,
are considered in the case where the viscosity is neglected and the periodic boundary condition is imposed. The equation possesses
two nonlinear terms: the convection and stretching terms. We prove that the solution exists globally in time if the stretching
term is weak in the sense to be specified below. We also discuss on blow-up solutions when the stretching term is strong.
Partly supported by the Grant-in-Aid for Scientific Research from JSPS No. 14204007. 相似文献
10.
A compressible Stokes system is studied in a polygon with one concave vertex. A corner singularity expansion is obtained up
to second order. The expansion contains the usual corner singularity functions for the velocity plus an “associated” velocity
singular function, and a pressure singular function. In particular the singularity of pressure is not local but occurs along
the streamline emanating from the incoming concave vertex. It is observed that certain first derivatives of the pressure become
infinite along the streamline of the ambient flow emanating from the concave vertex. Higher order regularity is shown for
the remainder.
This work was supported by the Com2MaC-SRC/ERC program of MOST/KOSEF (grant R11-1999-054), and by the U.S. National Science
Foundation. 相似文献
11.
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
12.
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.
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13.
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.
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14.
15.
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
16.
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.
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17.
The Navier–Stokes system with damping, which is motivated by Stommel–Charney model of ocean circulation, is considered in
a large elongated periodic rectangular domain with area of the order α−1, as α → 0. We obtain estimates for the dimension of the global attractor that are sharp as both α → 0 and ν → 0, where ν is the viscosity coefficient.
This work was supported in part by the US Civilian Research and Development Foundation, grant no. RUM1-2654-MO-05 (A.A.I.
and E.S.T.). The work of A.A.I. was supported in part by the Russian Foundation for Fundamental Research, grants no. 06-001-0096
and no. 05-01-429, and by the RAS Programme no. 1 ‘Modern problems of theoretical mathematics’. The work of E.S.T. was supported
in part by the NSF, grant no. DMS-0204794, the MAOF Fellowship of the Israeli Council of Higher Education, and by the BSF,
grant no. 200423. 相似文献
18.
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
19.
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
20.
We consider spectral semi-Galerkin approximations for the strong solutions of the nonhomogeneous Navier–Stokes equations.
We derive an optimal uniform in time error bound in the H1 norm for approximations of the velocity. We also derive an error estimate for approximations of the density in some spaces
Lr.
P. Braz e Silva was supported for this work by FAPESP/Brazil, #02/13270-1 and is currently supported in part by CAPES/MECD-DGU
Brazil/Spain, #117/06. M. Rojas-Medar is partially supported by CAPES/MECD-DGU Brazil/Spain, #117/06 and project BFM2003-06446-CO-01,
Spain. 相似文献