Statistical study of Navier-Stokes equations, I

C. Foiaş

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Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations

Ciprian Foias, Ricardo M. S. Rosa, Roger Temam (2013)

Annales de l’institut Fourier

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This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied....

Statistical study of Navier-Stokes equations, II

C. Foias (1973)

Rendiconti del Seminario Matematico della Università di Padova

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The Stokes system in the incompressible case-revisited

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.

Global solutions, structure of initial data and the Navier-Stokes equations

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. ...

On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation

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.

Some remarks on variants of the Navier-Stokes equations

R. H. Dyer, D. E. Edmunds (1971)

Colloquium Mathematicae

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Higher order estimates in further dimensions for the solutions of Navier-Stokes equations

Michael Wiegner (2003)

Banach Center Publications

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The resolution of the Navier-Stokes equations in anisotropic spaces.

Dragos Iftimie (1999)

Revista Matemática Iberoamericana

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In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are H in the i-th direction, δ + δ + δ = 1/2, -1/2 < δ < 1/2 and in a space which is L in the first two directions and B in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.

Global regularity for the 3D inhomogeneous incompressible Navier-Stokes equations with damping

Kwang-Ok Li, Yong-Ho Kim (2023)

Applications of Mathematics

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This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible Navier-Stokes equations with damping to inhomogeneous viscous incompressible fluids. ...

Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity

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.

Existence of regular solutions to the steady Navier-Stokes equations in bounded six-dimensional domains

Jens Frehse, Michael Růžička (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Global attractor for the Navier-Stokes equations in a cylindrical pipe

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.