Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

INTEGRANTES EQUIPO DE EDUCACIÓN VIAL EN MADRID [Material gráfico]

Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201

An Approximation Method for Non-Stationary Stokes Flow

We consider a rst order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R³. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hᵐ(G) (m = 0, 1, 2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity.</jats:p

The unsteady flow of a third-grade fluid caused by the periodic motion of an infinite wall with transpiration

AbstractIn this work, the unidirectional flow of an incompressible electrically conducting third-grade fluid past a vertical transpiration wall through a porous medium with time-dependent periodic motion is presented. The nonlinear partial differential equations are transformed to ordinary differential equation by means of symmetry reductions. The reduced equation is then solved analytically for steady-state and time-dependent transient parts. The time series of the transient flow velocity for different pertinent parameters are examined through plots. During the course of computation, it was observed that the time-dependent transient and steady-state solutions agree very well at large value of time when the ratio is related to fluid parameters γ∗γ>1

Time stepping procedures for the nonstationary Stokes equations

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman