Singularidades para as solu\c{c}\~{o}es das Equa\c{c}\~{o}es de Navier-Stokes and Euler e o Problema do Mil\^{e}nio

The purpose of this note is to offer a birds-eye view on the history and the state-of-the-art in the research surrounding the Millenium Prize problem for the Navier-Stokes equations, the general problem of singularities in fluid dynamics and the corresponding problem for the Euler equations. This is the content of a plenary talk delivered at the 2024 Biannual meeting of the Brazilian Math Society by Helena Nussenzveig Lopes and it is written in portuguese.