Solvability of the Navier-Stokes equations on manifolds with boundary.
Volker Priebe (1994)
Manuscripta mathematica
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Volker Priebe (1994)
Manuscripta mathematica
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Reinhard Farwig (1996)
Manuscripta mathematica
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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.
Yasushi Taniuchi (1997)
Manuscripta mathematica
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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.
R. Verfürth (1991)
Numerische Mathematik
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David Gérard-Varet, Nader Masmoudi (2013-2014)
Séminaire Laurent Schwartz — EDP et applications
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These notes are an introduction to the recent paper [7], about the well-posedness of the Prandtl equation. The difficulties and main ideas of the paper are described on a simpler linearized model.
Vladimir Shelukhin (1993)
Manuscripta mathematica
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Jan Prüss, Gieri Simonett (2009)
Banach Center Publications
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The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.
Gabriel R. Barrenechea, Patrick Le Tallec, Frédéric Valentin (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are...
V.A. Solonnikov (1995)
Mathematische Annalen
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Hideo Kozono, T. Ogawa, H. Sohr (1992)
Manuscripta mathematica
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M. Wiegner, W. M. Zajączkowski (2005)
Banach Center Publications
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The existence of global regular axially symmetric solutions to Navier-Stokes equations in a bounded cylinder and for boundary slip conditions is proved. Next, stability of these solutions is shown.
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.
Piotr Bogusław Mucha (2005)
Banach Center Publications
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We investigate the inviscid limit for the stationary Navier-Stokes equations in a two dimensional bounded domain with slip boundary conditions admitting nontrivial inflow across the boundary. We analyze admissible regularity of the boundary necessary to obtain convergence to a solution of the Euler system. The main result says that the boundary of the domain must be at least C²-piecewise smooth with possible interior angles between regular components less than π.
Paweł Konieczny (2006)
Colloquium Mathematicae
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The paper examines the steady Navier-Stokes equations in a three-dimensional infinite pipe with mixed boundary conditions (Dirichlet and slip boundary conditions). The velocity of the fluid is assumed to be constant at infinity. The main results show the existence of weak solutions with no restriction on smallness of the flux vector and boundary conditions.