Higher derivatives estimate for the 3D Navier–Stokes equation
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, p. 1189-1204
In this article, a nonlinear family of spaces, based on the energy dissipation, is introduced. This family bridges an energy space (containing weak solutions to Navier–Stokes equation) to a critical space (invariant through the canonical scaling of the Navier–Stokes equation). This family is used to get uniform estimates on higher derivatives to solutions to the 3D Navier–Stokes equations. Those estimates are uniform, up to the possible blowing-up time. The proof uses blow-up techniques. Estimates can be obtained by this means thanks to the galilean invariance of the transport part of the equation.
DOI : https://doi.org/10.1016/j.anihpc.2010.05.002
Classification:  76D05,  35Q30
Keywords: Navier–Stokes equation, Fluid mechanics, Blow-up techniques
@article{AIHPC_2010__27_5_1189_0,
author = {Vasseur, Alexis},
title = {Higher derivatives estimate for the 3D Navier--Stokes equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {27},
number = {5},
year = {2010},
pages = {1189-1204},
doi = {10.1016/j.anihpc.2010.05.002},
zbl = {05800075},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2010__27_5_1189_0}
}

Vasseur, Alexis. Higher derivatives estimate for the 3D Navier–Stokes equation. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, pp. 1189-1204. doi : 10.1016/j.anihpc.2010.05.002. http://www.numdam.org/item/AIHPC_2010__27_5_1189_0/

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