| Issue |
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
|
|
|---|---|---|
| Page(s) | 273 - 285 | |
| DOI | https://doi.org/10.1051/cocv:2002021 | |
| Published online | 15 August 2002 | |
On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space
1
Centre de Mathématiques et de leurs Applications, ENS de Cachan, 61 avenue du Président
Wilson, 94235 Cachan Cedex, France; brandole@cmla.ens-cachan.fr.
2
Équipe Modal'X, bâtiment G, Université de Paris X – Nanterre, 200 avenue
de la République, 92001 Nanterre Cedex, France.
3
Centre de Mathématiques et de leurs Applications, ENS de Cachan, 61 avenue du Président
Wilson, 94235 Cachan Cedex, France; ymeyer@cmla.ens-cachan.fr.
Received:
23
November
2001
Revised:
13
December
2001
We consider the spatial behavior of the velocity field u(x, t)
of a fluid filling the whole space 
(
) for arbitrarily small values of the
time variable.
We improve previous results on the spatial spreading by deducing the necessary
conditions 
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.
Mathematics Subject Classification: 35B40 / 76D05 / 35Q30
Key words: Navier–Stokes equations / space-decay / symmetries.
© EDP Sciences, SMAI, 2002
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