Solvability of a three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system
V. Solonnikov (1983)
Banach Center Publications
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V. Solonnikov (1983)
Banach Center Publications
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Zubelevich, Oleg (2005)
Lobachevskii Journal of Mathematics
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Cristescu, I.A. (2000)
APPS. Applied Sciences
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R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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Chebotarev, A. Yu. (2002)
Sibirskij Matematicheskij Zhurnal
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Claus Gerhardt (1979)
Mathematische Zeitschrift
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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.
Michael Wiegner (2003)
Banach Center Publications
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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...
M.D. Gunzburger, J.S. Peterson (1983)
Numerische Mathematik
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Jens Frehse, Michael Růžička (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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V.A. Solonnikov (1995)
Mathematische Annalen
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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.
Y. Maday, A. Quarteroni, C. Canuto (1984)
Numerische Mathematik
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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.