We consider the spatial behavior of the velocity field 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 . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
Classification : 35B40, 76D05, 35Q30
Mots clés : Navier-Stokes equations, space-decay, symmetries
@article{COCV_2002__8__273_0, 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 = {www.numdam.org/item/COCV_2002__8__273_0/} }
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/item/COCV_2002__8__273_0/
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