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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V. Solonnikov (1983)
Banach Center Publications
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Claus Gerhardt (1979)
Mathematische Zeitschrift
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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.
Reinhard Farwig (1992)
Mathematische Zeitschrift
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R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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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...
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.
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.
Michael Wiegner (2003)
Banach Center Publications
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M.D. Gunzburger, J.S. Peterson (1983)
Numerische Mathematik
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A. Fettah, T. Gallouët, H. Lakehal (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.
M. Giaquinta, G. Modica (1982)
Journal für die reine und angewandte Mathematik
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Jens Frehse, Michael Ruzicka (1995)
Mathematische Annalen
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Jens Frehse, Michael Růžička (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Jiří Neustupa, Patrick Penel (2008)
Banach Center Publications
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We formulate a boundary value problem for the Navier-Stokes equations with prescribed u·n, curl u·n and alternatively (∂u/∂n)·n or curl²u·n on the boundary. We deal with the question of existence of a steady weak solution.