Lq - Lr estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in Lq spaces.
Hirokazu Iwashita (1989)
Mathematische Annalen
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Hirokazu Iwashita (1989)
Mathematische Annalen
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V.A. Solonnikov (1995)
Mathematische Annalen
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Hideo Kozono, Takayoshi Ogawa (1993)
Mathematische Annalen
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Rodolfo Salvi (1988)
Mathematische Zeitschrift
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Wolfgang Borchers, Tetsuro Miyakawa (1988)
Mathematische Annalen
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R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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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.
Jens Frehse, Michael Ruzicka (1995)
Mathematische Annalen
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Michael Wiegner (2003)
Banach Center Publications
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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.
Burda, Pavel, Novotný, Jaroslav, Šístek, Jakub
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We present analytical solution of the Stokes problem in 2D domains. This is then used to find the asymptotic behavior of the solution in the vicinity of corners, also for Navier-Stokes equations in 2D. We apply this to construct very precise numerical finite element solution.
Michael Struwe (1995)
Mathematische Annalen
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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....
Geissert, M., Hieber, M.
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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.