On the regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137351We show that if a Leray-Hopf solution $u$ to the 3D Navier-Stokes equation belongs to $C((0,T]; B^{-1}_{\infty,\infty})$ or its jumps in the $B^{-1}_{\infty,\infty}$-norm do not exceed a constant multiple of viscosity, then $u$ is regular on $(0,T]$. Our method uses frequency local estimates on the nonlinear term, and yields an extension of the classical Ladyzhenskaya-Prodi-Serrin criterion.updated version -- a reference was added and a bug fixedAnalysis of PDEs76D03, 35Q30On the regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\infty,\infty}$text