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On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space

Published online by Cambridge University Press:  15 August 2002

Lorenzo Brandolese  and
Yves Meyer
Lorenzo Brandolese
Affiliation:
Centre de Mathématiques et de leurs Applications, ENS de Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex, France; [email protected]. Équipe Modal'X, bâtiment G, Université de Paris X – Nanterre, 200 avenue de la République, 92001 Nanterre Cedex, France.
Yves Meyer
Affiliation:
Équipe Modal'X, bâtiment G, Université de Paris X – Nanterre, 200 avenue de la République, 92001 Nanterre Cedex, France. Centre de Mathématiques et de leurs Applications, ENS de Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex, France; [email protected].
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Abstract

We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space $\xR^n$ ($n\ge2$) for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions $\int u_h(x,t)u_k(x,t)\,{\rm d}x=c(t)\delta_{h,k}$ under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.

Keywords

Navier–Stokes equationsspace-decaysymmetries.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 273 - 285
Copyright
© EDP Sciences, SMAI, 2002

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References

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