Letter to the editor.
Chebotarev, A. Yu. (2002)
Sibirskij Matematicheskij Zhurnal
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Chebotarev, A. Yu. (2002)
Sibirskij Matematicheskij Zhurnal
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Roger Temam, Xiaoming Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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V. Lovicar, I. Straškraba, A. Valli (1990)
Rendiconti del Seminario Matematico della Università di Padova
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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.
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.
V. Solonnikov (1983)
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...
Giovanni Prouse (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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A uniqueness criterion is given for the weak solution of the Navier-Stokes equations in the stationary case. Precisely, it is proved that, for a generic known term, there exists one and only one solution such that the mechanical power of the corresponding flow is maximum and that this maximum is "stable" in an appropriate sense.
M.D. Gunzburger, J.S. Peterson (1983)
Numerische Mathematik
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Piotr Kacprzyk (2010)
Annales Polonici Mathematici
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Global existence of regular special solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has already been shown. In this paper we prove the existence of the global attractor for the Navier-Stokes equations and convergence of the solution to a stationary solution.
Zubelevich, Oleg (2005)
Lobachevskii Journal of Mathematics
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Cristescu, I.A. (2000)
APPS. Applied Sciences
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Bernard Nowakowski, Wojciech M. Zajączkowski (2009)
Applicationes Mathematicae
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Global and regular solutions of the Navier-Stokes system in cylindrical domains have already been obtained under the assumption of smallness of (1) the derivative of the velocity field with respect to the variable along the axis of cylinder, (2) the derivative of force field with respect to the variable along the axis of the cylinder and (3) the projection of the force field on the axis of the cylinder restricted to the part of the boundary perpendicular to the axis of the cylinder....
Claus Gerhardt (1979)
Mathematische Zeitschrift
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Paweł Konieczny (2008)
Banach Center Publications
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The paper analyzes the issue of existence of solutions to linear problems in two dimensional exterior domains, linearizations of the Navier-Stokes equations. The systems are studied with a slip boundary condition. The main results prove the existence of distributional solutions for arbitrary data.