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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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.
Ewa Zadrzyńska (2005)
Banach Center Publications
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In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.
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.
Solonnikov, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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David Gérard-Varet, Matthieu Hillairet (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.
Chebotarev, A. Yu. (2002)
Sibirskij Matematicheskij Zhurnal
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Jolanta Socała, Wojciech M. Zajączkowski (2012)
Applicationes Mathematicae
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We examine the Navier-Stokes equations with homogeneous slip boundary conditions coupled with the heat equation with homogeneous Neumann conditions in a bounded domain in ℝ³. The domain is a cylinder along the x₃ axis. The aim of this paper is to show long time estimates without assuming smallness of the initial velocity, the initial temperature and the external force. To prove the estimate we need however smallness of the L₂ norms of the x₃-derivatives of these three quantities. ...
David Gérard-Varet, Matthieu Hillairet (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.
David Gérard-Varet, Matthieu Hillairet (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.
Jürgen Socolowsky (2008)
Banach Center Publications
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Viscous two-fluid flows arise in different kinds of coating technologies. Frequently, the corresponding mathematical models represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In this review article we present some results about nonisothermal stationary as well as about isothermal evolutionary viscous flow problems. The temperature-depending problems are characterized by coupled heat- and mass transfer and also by thermocapillary...
Roger Temam, Xiaoming Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
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...
Ersoy, Mehmet
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We present the full derivation of a one-dimensional free surface pipe or open channel flow model including friction with non constant geometry. The free surface model is obtained from the three-dimensional incompressible Navier-Stokes equations under shallow water assumptions with prescribed "well-suited" boundary conditions.