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Guillaume Valette (2015)
Annales Polonici Mathematici
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A stratified form is a collection of forms defined on the strata of a stratification of a subanalytic set and satisfying a continuity property when we pass from one stratum to another. We prove that these forms satisfy Stokes' formula on subanalytic singular simplices.
R. H. Dyer, D. E. Edmunds (1971)
Colloquium Mathematicae
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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.
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.
Jason S. Howell, Noel J. Walkington (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed.
Hermann Sohr, Wolf von Wahl (1984/85)
Manuscripta mathematica
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Crispo, F., Maremonti, P. (2004)
Zapiski Nauchnykh Seminarov POMI
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Jishan Fan, Xuanji Jia, Yong Zhou (2019)
Applications of Mathematics
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This paper proves a logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain with the Navier-type boundary condition.
Chelkak, S., Koshelev, A., Oganesyan, L. (1997)
Memoirs on Differential Equations and Mathematical Physics
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Zujin Zhang, Weijun Yuan, Yong Zhou (2019)
Applications of Mathematics
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We review the developments of the regularity criteria for the Navier-Stokes equations, and make some further improvements.
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.
G. Wittum (1989)
Numerische Mathematik
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Zujin Zhang, Chupeng Wu, Yong Zhou (2019)
Czechoslovak Mathematical Journal
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This paper concerns improving Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system, in the sense of multiplying certain negative powers of scaling invariant norms.
Claus Gerhardt (1979)
Mathematische Zeitschrift
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Marzia Bisi, Laurent Desvillettes (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in...
Zubelevich, Oleg (2005)
Lobachevskii Journal of Mathematics
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Yau, Horng-Tzer (1998)
Documenta Mathematica
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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.