Typicality results for weak solutions of the incompressible Navier--Stokes equations

Abstract

In this work we show that, in the class of $L^{\infty }((0,T);L^2({\mathbb{T}}^3))$ distributional solutions of the incompressible Navier-Stokes system, the ones which are smooth in some open interval of times are meagre in the sense of Baire category, and the Leray ones are a nowhere dense set.

20 pages