Displaying similar documents to “The resolution of the Navier-Stokes equations in anisotropic spaces.”

A generalization of a theorem by Kato on Navier-Stokes equations.

Marco Cannone (1997)

Revista Matemática Iberoamericana

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We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,∞);L(R)). More precisely, we show that if the initial data are sufficiently oscillating, in a suitable Besov space, then Kato's solution exists globally. As a corollary to this result, we obtain a theory of existence of self-similar solutions for the Navier-Stokes equations.

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. ...

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.