On the instantaneous spreading for the Navier-Stokes system in the whole space
ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), pp. 273-285.

We consider the spatial behavior of the velocity field $u\left(x,t\right)$ of a fluid filling the whole space ${ℝ}^{n}$ ($n\ge 2$) for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions $\int {u}_{h}\left(x,t\right){u}_{k}\left(x,t\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x=c\left(t\right){\delta }_{h,k}$ 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.

DOI: 10.1051/cocv:2002021
Classification: 35B40,  76D05,  35Q30
Keywords: Navier-Stokes equations, space-decay, symmetries
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title = {On the instantaneous spreading for the {Navier-Stokes} system in the whole space},
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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, Volume 8 (2002), pp. 273-285. doi : 10.1051/cocv:2002021. http://archive.numdam.org/articles/10.1051/cocv:2002021/

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