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.
Wu, Delin (2010)
Discrete Dynamics in Nature and Society
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Piotr Kacprzyk (2010)
Applicationes Mathematicae
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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.
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....
Geissert, M., Hieber, M.
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Mahdi Boukrouche, Grzegorz Łukaszewicz (2008)
Banach Center Publications
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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.
Michael Wiegner (2003)
Banach Center Publications
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Roger Temam, Xiaoming Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
Olga Ladyzhenskaya (1991-1992)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Kwang-Ok Li, Yong-Ho Kim (2023)
Applications of Mathematics
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This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible Navier-Stokes equations with damping to inhomogeneous viscous incompressible fluids. ...
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. ...