On the size of the regular set of suitable weak solutions of the Navier–Stokes equation

Lucà, Renato

Journées équations aux dérivées partielles (2015), article no. 5, 14 p.

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 ${\left[L^2\left({ℝ}^3\right)\right]}^3$ 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.

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