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Renato Lucà
On the size of the regular set of suitable weak solutions of the Navier–Stokes equation
Journées équations aux dérivées partielles (2015), Exp. No. 5, 14 p., doi: 10.5802/jedp.634
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Class. Math.: 35Q30, 35K55

Résumé - Abstract

We investigate the size of the regular set of weak solutions of the Navier–Stokes equation which are close, in an appropriate sense, to strong solutions. More precisely, if $w$ is a strong solution with initial datum $w_0$, we focus on weak solutions evolving by initial data $u_0$ such that the difference $u_0 - w_0$ is small in the weighted $[L^{2}(\mathbb{R}^{3})]^{3}$ space with weight $|x|^{-1}$. This is different by any smallness assumption in translation invariant critical Banach spaces. We also prove similar results in the small data setting.

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