# Mathematics Colloquia and Seminars

The talk addresses a question concerning the behaviour of a sequence of global solutions to the Navier-Stokes equations, with the corresponding sequence of smooth initial data being bounded in (non-energy classes) like Lebesgue space $L_3$ or weak Lebesgue space $L^{3,\infty}$. It is closely related to the question of what would be a reasonable definition of global weak solutions with a non-energy class of initial data, including the aforementioned Lebesgue spaces, whose norms are both scale invariant with the respect to the Navier-Stokes scaling.