Regularity of weak solutions to the Navier–Stokes equations in exterior domains

Abstract

Let u be a weak solution of the Navier–Stokes equations in an exterior domain \({\Omega \subset \mathbb{R}^3}\) and a time interval [0, T[ , 0 1}\), then u is regular at t. The same conclusion holds when the kinetic energy \({\frac{1}{2}\| u(t) \|_2^2}\) is locally Holder continuous with exponent \({\alpha > \frac{1}{2}}\).