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.
Chérif Amrouche, Patrick Penel, Nour Seloula (2013)
Annales mathématiques Blaise Pascal
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This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.
Joanna Rencławowicz, Wojciech M. Zajączkowski (2006)
Applicationes Mathematicae
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We prove the existence of weak solutions to the Navier-Stokes equations describing the motion of a fluid in a Y-shaped domain.
Francis Ribaud (2002)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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...
R. Farwig, H. Kozono, H. Sohr (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Aycil Cesmelioglu, Vivette Girault, Béatrice Rivière (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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A weak solution of the coupling of time-dependent incompressible Navier–Stokes equations with Darcy equations is defined. The interface conditions include the Beavers–Joseph–Saffman condition. Existence and uniqueness of the weak solution are obtained by a constructive approach. The analysis is valid for weak regularity interfaces.
Beirão da Veiga, H. (1997)
Portugaliae Mathematica
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K. K. Golovkin, A. Krzywicki (1967)
Colloquium Mathematicae
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Patrick Penel, Milan Pokorný (2004)
Applications of Mathematics
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We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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Michael Wiegner (2003)
Banach Center Publications
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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.