Asymptotic behavior of solutions to the compressible Navier-Stokes equations on the half space
Yoshiyuki Kagei, Takayuki Kobayashi (2005)
Banach Center Publications
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Yoshiyuki Kagei, Takayuki Kobayashi (2005)
Banach Center Publications
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Milan Pokorný (2005)
Banach Center Publications
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We review several regularity criteria for the Navier-Stokes equations and prove some new ones, containing different components of the velocity gradient.
Dongho Chae (2006)
Banach Center Publications
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We present regularity conditions for a solution to the 3D Navier-Stokes equations, the 3D Euler equations and the 2D quasigeostrophic equations, considering the vorticity directions together with the vorticity magnitude. It is found that the regularity of the vorticity direction fields is most naturally measured in terms of norms of the Triebel-Lizorkin type.
Piotr Kacprzyk (2010)
Applicationes Mathematicae
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Existence of a global attractor for the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has been shown already. In this paper we prove the higher regularity of the attractor.
Crispo, F., Maremonti, P. (2004)
Zapiski Nauchnykh Seminarov POMI
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K. K. Golovkin, A. Krzywicki (1967)
Colloquium Mathematicae
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Seregin, G.A., Shilkin, T.N., Solonnikov, V.N. (2004)
Journal of Mathematical Sciences (New York)
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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.
Patrick Penel, Milan Pokorný (2004)
Applications of Mathematics
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We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
M. Pulvirenti (2008)
Bollettino dell'Unione Matematica Italiana
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This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.
Elva Ortega-Torres, Marko Rojas-Medar (2009)
Rendiconti del Seminario Matematico della Università di Padova
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R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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Michael Wiegner (2003)
Banach Center Publications
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Zubelevich, Oleg (2005)
Lobachevskii Journal of Mathematics
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Piotr Bogusław Mucha (2008)
Banach Center Publications
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In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations. ...
Jens Frehse, Michael Růžička (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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