Asymptotic Behavior of Stokes Solutions in 2D Exterior Domains

We estimate L ^p spatial-temporal decay rates of solutions of the linearized equations of incompressible flow in a 2D exterior domain. When a domain has a boundary, pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary. To overcome the difficulty, we use a special form of a test function. The first author was supported by Korea Research Foundation Grant (KRF-2003-015-C00052), and the second author by KRF-2006-531-C0009.     

Steady Flows of Viscoelastic Fluids in Domains with Outlets to Infinity

The equations governing the motion of incompressible viscoelastic fluids of Rivlin—Ericksen and Oldroyd type are investigated in domains with cylindrical and paraboloidal outlets to infinity. For sufficiently small fluxes, prescribed in each outlet, existence and uniqueness of solutions are proven in weighted Hölder spaces. In domains with paraboloidal outlets the solution is obtained as a perturbation of the corresponding Navier—Stokes solution and in domains with cylindrical outlets as a perturbation of a flux carrier, constructed by joining together the exact solutions found in each outlet. These exact solutions are shown to be either rectilinear flows of Poiseuille type or flows composed of a rectilinear and of a transverse secondary component.     

Asymptotic Solution for a Kind of Boundary Layer Problem

This paper studies the partial differential equation with a small coefficient in the highest-order item. This kind of equation is also named as boundary layer problem. The Burgers equation and modified Burgers equation are analyzed in this approach. First, these equations are transferred into the strong nonlinear ones, and then the corresponding strong nonlinear equations are solved based on the perturbation method. The results from the asymptotic method are comparable with those obtained from numerical computation. An erratum to this article is available at .     

Physically Reasonable Solutions to Steady Compressible Navier-Stokes Equations in 2d Exterior Domains with Nonzero Velocity at Infinity

In a previous paper, the present authors studied the asymptotic behaviour of solutions to steady compressible Navier-Stokes equations in barotropic and isothermal regime with sufficiently small external data, in particular, in the whole plane. Here, the same problem is investigated in a two dimensional exterior domain with the prescribed velocity at infinity v_￥ 1 0 v_{\infty}\ne 0 . Similar results as in Dutto and Novotny [DuNo] are found; in particular, it is proved that there exists a unique solution which possesses the similar pointwise decay and the wake structure as the fundamental Oseen tensor.     

Boundary Stabilization of Stokes System in Exterior Domains

The problem of stabilizing a solution to the 2D Stokes system defined in the exterior of the bounded domain with smooth boundary is investigated, i.e. for a given initial velocity field and prescribed positive number k > 0 one has to construct a control function defined on the boundary such that the solution stabilizes to zero at the rate of 1/t ^k .     

Resolvent Estimates in L p for the Stokes Operator in Lipschitz Domains

We establish the L ^p resolvent estimates for the Stokes operator in Lipschitz domains in , for . The result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L ^p for (3/2) − ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320–334).     

幂硬化粘塑性材料动态扩展裂纹尖端场的渐近解

采用弹性－粘塑性本构模型，对幂硬化粘塑性介质中反平面剪切动态扩展裂纹尖端的应力，应变场进行了渐近分析，给出了反平面剪切动态扩展纹尖端场的渐进方程。分析结果表明，在裂纹法端应力具有（ｌｎＲ／ｒ）１／ｎ－１的奇异性，应变具有（ｌｎＲ／Ｒｎ／ｎ－１的奇异性。从而提示了幂硬化粘塑材料反平面剪动态扩展裂纹尖端场的渐近行为。     

应变损伤材料平面应力动态裂纹尖端场的渐近解

采用塑性动力学方程,对应变损伤材料的平面应力动态裂纹尖端场进行了渐近分析。假定损伤规律服从反比例关系,对平面应力问题,导出了本构方程,并给出了动态弹塑性场的渐近解,揭示了场的渐近特性。     

An Asymptotic Approach to the Torsion Problem in Thin Walled Beams

A rather straightforward derivation of the Γ-limit of the torsion problem as the thickness goes to zero is obtained for generic thin walled beams. The limit stresses are evaluated and the distributional nature of one of the stress components is clarified.      

Asymptotic Solution of the Problem of Heat Transfer between Two Plates and a Uniform Fluid Flow

For low Peclet numbers, analytic expressions are obtained for three highest terms of the asymptotic expansion of the solution of the convective heat-transfer problem for a system consisting of two parallel plates with identical lengths identical and constant surface temperatures and an infinite uniform fluid flow with a low Prandtl number.     

The Existence Problem for Steiner Networks in Strictly Convex Domains

We consider the existence problem for ‘Steiner networks’ (trivalent graphs with 2π/3 angles at each junction) in strictly convex domains, with ‘Neumann’ boundary conditions. For each of the three possible combinatorial possibilities, sufficient conditions on the domain are derived for existence. In addition, in each case explicit examples of nonexistence are given.     

On the Existence of Weak Solutions to the Steady Compressible Navier–Stokes Equations in Domains with Conical Outlets

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.     

The Solution of Saint-Venant's Problem in the Theory of Cosserat Shells

This paper is concerned with the linear theory of thin elastic shells modelled as Cosserat surfaces. We formulate the corresponding Saint-Venant's problem with respect to cylindrical shells. Then, we determine the solution of the relaxed problem for both open and closed cylindrical surfaces. The edge curves perpendicular to the generator are not necessarily circular. Finally, some particular cases are discussed.