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The Global Existence of Small Solutions to the oldroyd-b model

Chinese Annals of Mathematics,Series b 2011年第2期32卷 215-222页

作者： Wenjing ZHAO Department of Mathematics Northeastern University Shenyang 110819 China

The Cauchy problem to the oldroyd-b model is *** particular,it is shown that if the smooth solution （u,τ） to this system blows up at a finite time T～＊,then 0～T～＊u（t） L∞dt = ∞.Furthermore,the global existen... 详细信息

关键词： Cauchy problem oldroyd-b model Global existence

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Incompressible Limit of the oldroyd-b model with Density-Dependent Viscosity

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Journal of Applied Mathematics and Physics 2023年第4期11卷 949-971页

作者： Qingliu Li Dandan Ren School of Mathematics and big Data Anhui University of Science and Technology Huainan China

This paper studies the existence and uniqueness of local strong solutions to an oldroyd-b model with density-dependent viscosity in a bounded domain Ω ⊂ Rd, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.

关键词： Incompressible Limit oldroyd-b model Slip boundary Condition Density-Dependent Viscosity

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Linear instability of the electrified free interface between two cylindrical shells of viscoelastic fluids through porous media

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Acta Mechanica Sinica 2012年第6期28卷 1572-1589页

作者： Magdy A. Sirwah Department of Mathematics Faculty of Science Tanta University

In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial oldroyd-b fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence （de-stabilizing effects） depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.

关键词： Modified Darcy's law oldroyd-b model Cap-illary stability flow Insoluble surfactant Surface charges Porous media

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TRANSIENT EFFECT OF A bOGER FLUID FLOWING AROUND A CONFINED CYLINDER

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Chinese Journal of Polymer Science 2001年第4期19卷 377-384页

作者： Xian-feng Li Huai-tian bu De-lu Zhao State Key Laboratory of Polymer Physics and Chemistry Center for Molecular Science,Institute of Chemistry, Chinese Academy of Sciences, beijing 100080, China 中科院化学所高分子物理与化学国家重点实验室北京

This paper is concerned with the numerical simulation of the transient effect of an inertialess boger flow past a confined circular cylinder and the comparison of predictions with particle image velocimetry (PIV) measurements given by Shiang et al.. Dynamic simulation based on the oldroyd-b constitutive model was carried out using a Lagrangian-Eulerian algorithm. The evolution of velocity field was obtained for the flow at two Deborah (De) numbers, i.e. De = 1.2 and 3.0. At low De, the flow reached steady state rapidly, and showed a symmetric flow regime. However, at high De, the time required to reach steady flow behind the cylinder increased significantly, and the distribution of the velocity field appears to be asymmetric with respect to the stagnation line. Fairly good agreement between the numerical results and the experimental observations is reported. It can be concluded that both the experimental measurements and the present simulations indicate that the elasticity of the polymeric flow strongly affect the flow regime of viscoelastic flow around a confined cylinder.

关键词： transient effect flow around a cylinder Lagrangian-Eulerian algorithm oldroyd-b model

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