共查询到20条相似文献,搜索用时 15 毫秒
1.
H. Beiro da Veiga 《纯数学与应用数学通讯》2005,58(4):552-577
Navier‐Stokes equations with shear dependent viscosity under the classical non‐slip boundary condition have been introduced and studied, in the sixties, by O. A. Ladyzhenskaya and, in the case of gradient dependent viscosity, by J.‐L. Lions. A particular case is the well known Smagorinsky turbulence model. This is nowadays a central subject of investigation. On the other hand, boundary conditions of slip type seems to be more realistic in some situations, in particular in numerical applications. They are a main research subject. The existence of weak solutions u to the above problems, with slip (or non‐slip) type boundary conditions, is well known in many cases. However, regularity up to the boundary still presents many open questions. In what follows we present some regularity results, in the stationary case, for weak solutions to this kind of problems; see Theorems 3.1 and 3.2. The evolution problem is studied in the forthcoming paper [6]; see the remark at the end of the introduction. © 2004 Wiley Periodicals, Inc. 相似文献
2.
Christoph Scheven 《Calculus of Variations and Partial Differential Equations》2006,25(4):409-429
Let
and
be Riemannian manifolds,
compact without boundary. We develop a definition of a variationally harmonic map
with respect to a general boundary condition of the kind u(x)∊Γ(x) for a.e.
, where
are given submanifolds depending smoothly on x. The given definition of variationally harmonic maps is slightly more restrictive, but also more natural than the usual definition
of stationary harmonic maps. After deducing an energy monotonicity formula, it is possible to derive a regularity theory for
variationally harmonic maps with general boundary data. The results include full boundary regularity in the Dirichlet boundary
case Γ(x) = {g(x)} for
if
does not carry a nonconstant harmonic 2-sphere. 相似文献
3.
C. E. Garza-Hume 《Journal of Geometric Analysis》1997,7(1):83-107
We study the boundary regularity ofp-harmonic maps with free and partially constrained boundary conditions and give estimates on the size of the singular subset
of the boundary. 相似文献
4.
5.
T. Hayat Masood Khan M. Ayub 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(6):1012-1029
The assumption that a fluid adheres to a solid boundary (‘no-slip’ boundary condition) is one of the central tenets of the
Navier-Stokes theory. However, there are situations wherein this assumption does not hold. In this communication we examine
the effects of slip at the wall when an Oldroyd 6-constant fluid is considered in a channel. The slip assumed depends on the
shear stress at the wall. The three non-linear problems are solved using homotopy analysis method (HAM). The results for the
velocity profiles are presented and discussed.
Received: January 13, 2004; revised: September 7, 2004 相似文献
6.
We first represent the pressure in terms of the velocity in . Using this representation we prove that a solution to the Navier-Stokes equations is in under the critical assumption that , with r?3, while for r=3 the smallness is required. In [H.J. Choe, Boundary regularity of weak solutions of the Navier-Stokes equations, J. Differential Equations 149 (2) (1998) 211-247], a boundary L∞ estimate for the solution is derived if the pressure on the boundary is bounded. In our work, we remove the boundedness assumption of the pressure. Here, our estimate is local. Indeed, employing Moser type iteration and the reverse Hölder inequality, we find an integral estimate for L∞-norm of u. 相似文献
7.
Aibin Zang 《中国科学 数学(英文版)》2018,61(4):727-744
This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough. 相似文献
8.
《Journal of Computational and Applied Mathematics》2002,149(1):57-69
This paper is concerned with the stationary and nonstationary flow of viscous incompressible fluid under boundary conditions of friction type, which are certain nonlinear boundary conditions similar to the so-called Signorini boundary condition in elasticity. We assume that the flow is governed by the linear Stokes equation, while the boundary condition is nonlinear. From the methodological viewpoint, the analysis is carried out in a coherent way, starting from study of the related boundary value problems for the stationary flow by means of the theory of variational inequalities, and getting to wellposedness of the initial boundary value problems for the nonstationary flow by means of the nonlinear semigroup theory. From the viewpoint of applications, we mention original motivations and include some new generalizations like the cases of anisotropic friction and inhomogeneous boundary value. 相似文献
9.
Sergueï A. Nazarov Adélia Sequeira Maria Specovius-Neugebauer Juha H. Videman 《Mathematical Methods in the Applied Sciences》2008,31(8):937-958
The steady three-dimensional exterior flow of a viscoelastic non-Newtonian fluid is approximated by reducing the corresponding nonlinear elliptic–hyperbolic system to a bounded domain. On the truncation surface with a large radius R, nonlinear, local second-order artificial boundary conditions are constructed and a new concept of an artificial transport equation is introduced. Although the asymptotic structure of solutions at infinity is known, certain attributes cannot be found explicitly so that the artificial boundary conditions must be constructed with incomplete information on asymptotics. To show the existence of a solution to the approximation problem and to estimate the asymptotic precision, a general abstract scheme, adapted to the analysis of coupled systems of elliptic–hyperbolic type, is proposed. The error estimates, obtained in weighted Sobolev norms with arbitrarily large smoothness indices, prove an approximation of order O(R−2+ε), with any ε>0. Our approach, in contrast to other papers on artificial boundary conditions, does not use the standard assumptions on compactly supported right-hand side f, leads, in particular, to pointwise estimates and provides error bounds with constants independent of both R and f. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
10.
The forces experienced by randomly and homogeneously distributed parallel circular cylinder or spheres in uniform viscous
flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the
result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but
little in shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the first
order in the small parameter characterizing the deformation. As a particular case of this we considered an oblate spheroid
and evaluate the drag on it. 相似文献
11.
R. Ellahi T. Hayat F. M. Mahomed A. Zeeshan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,71(2):877-888
In this article, we use nonlinear slip conditions to investigate three fundamental flows. Constitutive equations of the third
grade fluid give rise to nonlinear equations. Exact analytic solutions of the nonlinear equations with nonlinear boundary
conditions are developed. Numerical values between the dimensionless third grade and slip parameters are tabulated. Graphs
are plotted and discussed. 相似文献
12.
R. Ellahi T. Hayat F. M. Mahomed A. Zeeshan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,61(5):877-888
In this article, we use nonlinear slip conditions to investigate three fundamental flows. Constitutive equations of the third grade fluid give rise to nonlinear equations. Exact analytic solutions of the nonlinear equations with nonlinear boundary conditions are developed. Numerical values between the dimensionless third grade and slip parameters are tabulated. Graphs are plotted and discussed. 相似文献
13.
In this work, we study the Brinkman–Forchheimer equations driven under slip boundary conditions of friction type. We prove the existence and uniqueness of weak solutions by means of regularization combined with the Faedo-Galerkin approach. Next, we discuss the continuity of the solution with respect to Brinkman’s and Forchheimer’s coefficients. Finally, we show that the weak solution of the corresponding stationary problem is stable. 相似文献
14.
D. Palaniappan P. Daripa 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2002,46(1):281-307
Steady two-dimensional creeping flows induced by line singularities in the presence of an infinitely long circular cylinder with stick-slip boundary conditions are examined. The singularities considered here include a rotlet, a potential source and a stokeslet located outside a cylinder and lying in a plane containing the cylinder axis. The general exterior boundary value problem is formulated and solved in terms of a stream function by making use of the Fourier expansion method. The solutions for various singularity driven flows in the presence of a cylinder are derived from the general results. The stream function representation of the solutions involves a definite integral whose evaluation depends on a non-dimensional slip parameter l1\lambda_1. For extremal values, l1 = 0\lambda_1 = 0 and l1 = 1\lambda_1 = 1, of the slip parameter our results reduce to solutions of boundary value problems with stick (no-slip) and perfect slip conditions, respectively.¶The slip parameter influences the flow patterns significantly. The plots of streamlines in each case show interesting flow patterns. In particular, in the case of a single rotlet/stokeslet (with axis along y-direction) flows, eddies are observed for various values of l1\lambda_1. The flow fields for a pair of singularities located on either side of the cylinder are also presented. In these flows, eddies of different sizes and shapes exist for various values of l1\lambda_1 and the singularity locations. Plots of the fluid velocity on the surface show locations of the stagnation points on the surface of the cylinder and their dependencies on l1\lambda_1 and singularity locations. 相似文献
15.
16.
Ben‐yu Guo 《Mathematical Methods in the Applied Sciences》2008,31(5):607-626
In this paper, we consider incompressible viscous fluid flows with slip boundary conditions. We first prove the existence of solutions of the unsteady Navier–Stokes equations in n‐spacial dimensions. Then, we investigate the stability, uniqueness and regularity of solutions in two and three spacial dimensions. In the compactness argument, we construct a special basis fulfilling the incompressibility exactly, which leads to an efficient and convergent spectral method. In particular, we avoid the main difficulty for ensuring the incompressibility of numerical solutions, which occurs in other numerical algorithms. We also derive the vorticity‐stream function form with exact boundary conditions, and establish some results on the existence, stability and uniqueness of its solutions. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
17.
R. Ellahi 《Communications in Nonlinear Science & Numerical Simulation》2009,14(4):1377-1384
We examine the consequences of the slip at the plates on the flows of an Oldroyd 8-constant fluid. The governing non-linear boundary value problems are solved by using homotopy analysis method (HAM). Physical significance of the results is also given. 相似文献
18.
L. Consiglieri 《Annali di Matematica Pura ed Applicata》2008,187(4):647-665
This work adresses an unsteady heat flow problem involving friction and convective heat transfer behaviors on a part of the
boundary. The problem is constituted by a variational motion inequality with energy dependent coefficients, and the energy
equation in the framework of L
1-theory for the dissipative term. Using the duality theory of convex analysis, it also envolves the existence of Lagrange
multipliers. Weak solutions of an approximate coupled system are proven by a fixed point argument for multivalued mappings
and compactness methods. Then the existence result for the initial coupled system is proven by the passage to the limit.
This work was partially supported by FCT research program POCTI (Portugal/FEDER-EU). 相似文献
19.
Many far field boundary conditions are proposed in the literature to solve Navier-Stokes equations. It is necessary to distinguish the streamwise or outlet boundary conditions and the spanwise boundary conditions. In the first case the flow crosses the artificial frontier and it is required to avoid reflections that can change significantly the flow. In the second case the Navier-slip boundary condition is often used but if the frontier is not far enough the boundary is both inlet and outlet. Thus the Navier-slip boundary condition is not well suited as it imposes no flux through the frontier. The aim of this work is to compare some well-known boundary conditions, to quantify to which extend the artificial frontier can be close to the bodies in two- and three-dimensions and to take into account the flow rate through the spanwise directions. 相似文献
20.
E. S. Baranovskii 《Journal of Applied and Industrial Mathematics》2014,8(2):168-176
Some optimal control problem is studied for the stationary motion equations for the Jeffreys medium with the slip condition of the Navier type on the boundary. The control parameter is the external force. The existence of a weak solution is proven minimizing a given cost functional. Some properties of the solution set of the optimization problem are established. 相似文献