On the instantaneous spreading for the Navier-Stokes system in the whole space

Brandolese, Lorenzo; Meyer, Yves

doi:10.1051/cocv:2002021

Brandolese, Lorenzo ; Meyer, Yves

ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 273-285.

Résumé

We consider the spatial behavior of the velocity field $u (x, t)$ of a fluid filling the whole space $ℝ^{n}$ ( $n \geq 2$ ) for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions $\int u_{h} (x, t) u_{k} (x, t) d x = c (t) δ_{h, k}$ 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.

Zbl

DOI : 10.1051/cocv:2002021

Classification : 35B40, 76D05, 35Q30
Mots-clés : Navier-Stokes equations, space-decay, symmetries

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     author = {Brandolese, Lorenzo and Meyer, Yves},
     title = {On the instantaneous spreading for the {Navier-Stokes} system in the whole space},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {273--285},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     doi = {10.1051/cocv:2002021},
     zbl = {1080.35063},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2002021/}
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Brandolese, Lorenzo; Meyer, Yves. On the instantaneous spreading for the Navier-Stokes system in the whole space. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 273-285. doi : 10.1051/cocv:2002021. http://www.numdam.org/articles/10.1051/cocv:2002021/

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