Displaying similar documents to “Regularity properties of the attractor to the Navier-Stokes equations”

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

Piotr Kacprzyk (2010)

Annales Polonici Mathematici

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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.

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

M. Pulvirenti (2008)

Bollettino dell'Unione Matematica Italiana

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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.

Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder

Piotr Kacprzyk (2009)

Applicationes Mathematicae

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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. To prove the long time existence we need smallness of derivatives, with respect to the variable along the axis of the cylinder, of the external force and of the initial velocity in L₂-norms. Moreover, we need smallness of derivatives of inflow and outflow with respect to tangent directions to the boundary...

On the conditional regularity of the Navier-Stokes and related equations

Dongho Chae (2006)

Banach Center Publications

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We present regularity conditions for a solution to the 3D Navier-Stokes equations, the 3D Euler equations and the 2D quasigeostrophic equations, considering the vorticity directions together with the vorticity magnitude. It is found that the regularity of the vorticity direction fields is most naturally measured in terms of norms of the Triebel-Lizorkin type.

The Stokes system in the incompressible case-revisited

Rainer Picard (2008)

Banach Center Publications

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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.

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

Piotr Bogusław Mucha (2008)

Banach Center Publications

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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. ...

Global attractor for Navier-Stokes equations in cylindrical domains

Bernard Nowakowski, Wojciech M. Zajączkowski (2009)

Applicationes Mathematicae

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

Piotr Kacprzyk (2007)

Applicationes Mathematicae

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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...

Lagrangian approximations and weak solutions of the Navier-Stokes equations

Werner Varnhorn (2008)

Banach Center Publications

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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

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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...