On regularity of stationary solutions to the Navier-Stokes equation in 3D torus.
Zubelevich, Oleg (2005)
Lobachevskii Journal of Mathematics
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Zubelevich, Oleg (2005)
Lobachevskii Journal of Mathematics
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R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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Claus Gerhardt (1979)
Mathematische Zeitschrift
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Chebotarev, A. Yu. (2002)
Sibirskij Matematicheskij Zhurnal
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G. Wittum (1989)
Numerische Mathematik
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Michael Wiegner (2003)
Banach Center Publications
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Burda, Pavel, Novotný, Jaroslav, Šístek, Jakub
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We present analytical solution of the Stokes problem in 2D domains. This is then used to find the asymptotic behavior of the solution in the vicinity of corners, also for Navier-Stokes equations in 2D. We apply this to construct very precise numerical finite element solution.
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.
Jason S. Howell, Noel J. Walkington (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed.
M.D. Gunzburger, J.S. Peterson (1983)
Numerische Mathematik
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Michal Křížek (1990)
Banach Center Publications
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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.
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.
Jens Frehse, Michael Růžička (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Reinhard Farwig (1992)
Mathematische Zeitschrift
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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...
Jens Frehse, Michael Ruzicka (1995)
Mathematische Annalen
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