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Large, global solutions to the Navier-Stokes equations, slowly varying in one direction

Authors: Jean-Yves Chemin and Isabelle Gallagher
Journal: Trans. Amer. Math. Soc. 362 (2010), 2859-2873
MSC (2000): Primary 35Q30, 76D05, 76D03
Published electronically: January 20, 2010
MathSciNet review: 2592939
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Abstract: In two earlier papers by the authors, classes of initial data for the three dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large. The aim of this article is to provide new examples of arbitrarily large initial data giving rise to global solutions, in the whole space. Contrary to the previous examples, the initial data has no particular oscillatory properties, but varies slowly in one direction. The proof uses the special structure of the nonlinear term of the equation.

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Additional Information

Jean-Yves Chemin
Affiliation: Laboratoire J.-L. Lions UMR 7598, Université Paris VI, 175 rue du Chevaleret, 75013 Paris, France

Isabelle Gallagher
Affiliation: Institut de Mathématiques de Jussieu UMR 7586, Université Paris VII, 175 rue du Chevaleret, 75013 Paris, France

Keywords: Navier-Stokes equations, global wellposedness.
Received by editor(s): October 29, 2007
Published electronically: January 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society

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