All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 13 Next

Displaying 241 – 260 of 1082

Showing per page

Convolution of radius functions on ℝ³

Konstanty Holly (1994)

Annales Polonici Mathematici

We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in the boundary...

Coupling Darcy and Stokes equations for porous media with cracks

Christine Bernardi, Frédéric Hecht, Olivier Pironneau (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive...

Coupling Darcy and Stokes equations for porous media with cracks

Christine Bernardi, Frédéric Hecht, Olivier Pironneau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive...

Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations

Macarena Gómez Mármol, Francisco Ortegón Gallego (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and φ. The system presents nonlinear turbulent viscosity A ( θ , ϕ ) and nonlinear source terms of the form θ 2 | ∇ u | 2 and θ ϕ | ∇ u | 2 lying in L1. Some existence results are shown in this paper, including L ∞ -estimates and positivity for both θ and φ.

Criteria of local in time regularity of the Navier-Stokes equations beyond Serrin's condition

Reinhard Farwig, Hideo Kozono, Hermann Sohr (2008)

Banach Center Publications

Let u be a weak solution of the Navier-Stokes equations in a smooth bounded domain Ω ⊆ ℝ³ and a time interval [0,T), 0 < T ≤ ∞, with initial value u₀, external force f = div F, and viscosity ν > 0. As is well known, global regularity of u for general u₀ and f is an unsolved problem unless we pose additional assumptions on u₀ or on the solution u itself such as Serrin’s condition | | u | | L s ( 0 , T ; L q ( Ω ) ) < ∞ where 2/s + 3/q = 1. In the present paper we prove several local and global regularity properties by using assumptions...

Density-dependent incompressible fluids with non-Newtonian viscosity

F. Guillén-González (2004)

Czechoslovak Mathematical Journal

We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of p -coercivity and ( p - 1 ) -growth, for a given parameter p > 1 . The existence of Dirichlet weak solutions was obtained in [2], in the cases p ≥ 12 / 5 if d = 3 or p ≥ 2 if d = 2 , d being the dimension of the domain. In this paper, with help of some new estimates (which lead...

Derivation of the Reynolds equation for lubrication of a rotating shaft

Antonija Duvnjak, Eduard Marušić-Paloka (2000)

Archivum Mathematicum

In this paper, using the asymptotic expansion, we prove that the Reynolds lubrication equation is an approximation of the full Navier–Stokes equations in thin gap between two coaxial cylinders in relative motion. Boundary layer correctors are computed. The error estimate in terms of domain thickness for the asymptotic expansion is given. The corrector for classical Reynolds approximation is computed.

Distributed control for multistate modified Navier-Stokes equations

Nadir Arada (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality conditions.

Domain decomposition methods for solving the Burgers equation

Robert Cimrman (1999)

Applications of Mathematics

This article presents some results of numerical tests of solving the two-dimensional non-linear unsteady viscous Burgers equation. We have compared the known convergence and parallel performance properties of the additive Schwarz domain decomposition method with or without a coarse grid for the model Poisson problem with those obtained by experiments for the Burgers problem.

Currently displaying 241 – 260 of 1082