Displaying similar documents to “Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder”

Global attractor for Navier-Stokes equations in cylindrical domains

Bernard Nowakowski, Wojciech M. Zajączkowski (2009)

Applicationes Mathematicae

Similarity:

Global and regular solutions of the Navier-Stokes system in cylindrical domains have already been obtained under the assumption of smallness of (1) the derivative of the velocity field with respect to the variable along the axis of cylinder, (2) the derivative of force field with respect to the variable along the axis of the cylinder and (3) the projection of the force field on the axis of the cylinder restricted to the part of the boundary perpendicular to the axis of the cylinder....

Global attractor for the Navier-Stokes equations in a cylindrical pipe

Piotr Kacprzyk (2010)

Annales Polonici Mathematici

Similarity:

Global existence of regular special solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has already been shown. In this paper we prove the existence of the global attractor for the Navier-Stokes equations and convergence of the solution to a stationary solution.

Global regular nonstationary flow for the Navier-Stokes equations in a cylindrical pipe

Piotr Kacprzyk (2007)

Applicationes Mathematicae

Similarity:

Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. Global existence is proved in two steps. First, by the Leray-Schauder fixed point theorem we prove local existence with large existence time. Next, the local solution is prolonged step by step. The existence is proved without any restrictions on the magnitudes of the inflow, outflow, external force...

Global existence of solutions to Navier-Stokes equations in cylindrical domains

Bernard Nowakowski, Wojciech M. Zajączkowski (2009)

Applicationes Mathematicae

Similarity:

We prove the existence of global and regular solutions to the Navier-Stokes equations in cylindrical type domains under boundary slip conditions, where coordinates are chosen so that the x₃-axis is parallel to the axis of the cylinder. Regular solutions have already been obtained on the interval [0,T], where T > 0 is large, on the assumption that the L₂-norms of the third component of the force field, of derivatives of the force field, and of the velocity field with respect to the...

Global solutions, structure of initial data and the Navier-Stokes equations

Piotr Bogusław Mucha (2008)

Banach Center Publications

Similarity:

In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations. ...

Regularity properties of the attractor to the Navier-Stokes equations

Piotr Kacprzyk (2010)

Applicationes Mathematicae

Similarity:

Existence of a global attractor for the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has been shown already. In this paper we prove the higher regularity of the attractor.

On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation

M. Pulvirenti (2008)

Bollettino dell'Unione Matematica Italiana

Similarity:

This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.

The Stokes system in the incompressible case-revisited

Rainer Picard (2008)

Banach Center Publications

Similarity:

The classical Stokes system is reconsidered and reformulated in a functional analytical setting allowing for low regularity of the data and the boundary. In fact the underlying domain can be any non-empty open subset Ω of ℝ³. A suitable solution concept and a corresponding solution theory is developed.

On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition

Mahdi Boukrouche, Grzegorz Łukaszewicz (2008)

Banach Center Publications

Similarity:

We consider a two-dimensional Navier-Stokes shear flow with time dependent boundary driving and subject to Tresca law. We establish the existence of a unique global in time solution and then, using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set, we prove the existence of the pullback attractor for the associated cocycle. This research is motivated by a problem from lubrication theory.

Lagrangian approximations and weak solutions of the Navier-Stokes equations

Werner Varnhorn (2008)

Banach Center Publications

Similarity:

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles...

An application of the BDDC method to the Navier-Stokes equations in 3-D cavity

Hanek, Martin, Šístek, Jakub, Burda, Pavel

Similarity:

We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient...

Linear flow problems in 2D exterior domains for 2D incompressible fluid flows

Paweł Konieczny (2008)

Banach Center Publications

Similarity:

The paper analyzes the issue of existence of solutions to linear problems in two dimensional exterior domains, linearizations of the Navier-Stokes equations. The systems are studied with a slip boundary condition. The main results prove the existence of distributional solutions for arbitrary data.