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 ${\left[{L}^{2}\left({\mathbb{R}}^{3}\right)\right]}^{3}$ space with weight ${\left|x\right|}^{-1}$. This is different by any smallness assumption in translation invariant critical Banach spaces. We also prove similar results in the small data setting.

@article{JEDP_2015____A5_0, author = {Luc\`a, Renato}, title = {On the size of the regular set of suitable weak solutions of the {Navier{\textendash}Stokes} equation}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {5}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2015}, doi = {10.5802/jedp.634}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.634/} }

TY - JOUR AU - Lucà, Renato TI - On the size of the regular set of suitable weak solutions of the Navier–Stokes equation JO - Journées équations aux dérivées partielles PY - 2015 DA - 2015/// PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.634/ UR - https://doi.org/10.5802/jedp.634 DO - 10.5802/jedp.634 LA - en ID - JEDP_2015____A5_0 ER -

%0 Journal Article %A Lucà, Renato %T On the size of the regular set of suitable weak solutions of the Navier–Stokes equation %J Journées équations aux dérivées partielles %D 2015 %I Groupement de recherche 2434 du CNRS %U https://doi.org/10.5802/jedp.634 %R 10.5802/jedp.634 %G en %F JEDP_2015____A5_0

Lucà, Renato. On the size of the regular set of suitable weak solutions of the Navier–Stokes equation. Journées équations aux dérivées partielles (2015), article no. 5, 14 p. doi : 10.5802/jedp.634. http://www.numdam.org/articles/10.5802/jedp.634/

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