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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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.
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.
Frédéric Rousset (2012-2013)
Séminaire Laurent Schwartz — EDP et applications
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The aim of this talk is to present recent results obtained with N. Masmoudi on the free surface Navier-Stokes equations with small viscosity.
V.A. Solonnikov (1995)
Mathematische Annalen
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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.
Solonnikov, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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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.
Ewa Zadrzyńska
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The results concerning free boundary problems for both incompressible and compressible Navier-Stokes equations are reviewed in this paper.
R. Verfürth (1991)
Numerische Mathematik
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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...
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.
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.
R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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Piotr Kacprzyk (2009)
Applicationes Mathematicae
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Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. To prove the long time existence we need smallness of derivatives, with respect to the variable along the axis of the cylinder, of the external force and of the initial velocity in L₂-norms. Moreover, we need smallness of derivatives of inflow and outflow with respect to tangent directions to the boundary...