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Shapour Heidarkhani (2012)
Annales Polonici Mathematici
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Using a recent critical point theorem due to Bonanno, the existence of a non-trivial solution for a class of systems of n fourth-order partial differential equations with Navier boundary conditions is established.
Neustupa, Tomáš
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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.
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.
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.
Adauto Medeiros, Luis, Limaco Ferrel, Juan (1997)
Memoirs on Differential Equations and Mathematical Physics
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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.
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.
Seregin, G.A., Shilkin, T.N., Solonnikov, V.N. (2004)
Journal of Mathematical Sciences (New York)
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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.
Francis Ribaud (2002)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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R. Farwig, H. Kozono, H. Sohr (2011)
Rendiconti del Seminario Matematico della Università di Padova
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R. Verfürth (1991)
Numerische Mathematik
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W. M. Zajączkowski
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We examine the nonstationary Stokes system in a bounded domain with the boundary slip conditions. We assume that there exists a line which crosses the domain and that the data belong to Sobolev spaces with weights equal to some powers of the distance to the line. Then the existence of solutions in Sobolev spaces with the corresponding weights is proved.
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.
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.