A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain

Jishan Fan; Xuanji Jia; Yong Zhou

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Displaying similar documents to “A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain”

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We review the developments of the regularity criteria for the Navier-Stokes equations, and make some further improvements.

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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.

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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.

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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.

Boundary partial regularity for the Navier-Stokes equations.

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We formulate a boundary value problem for the Navier-Stokes equations with prescribed u·n, curl u·n and alternatively (∂u/∂n)·n or curl²u·n on the boundary. We deal with the question of existence of a steady weak solution.

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Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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