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Incompressible fluids are described by the Navier-Stokes equations. Yet, it is not yet known whether the Cauchy problem is well posed for these equations, and whether solutions of finite energy are regular or unique.From a practical point of view, two interesting questions arise: if there is a blow-up solution, what is his shape? Is there a loss of unicity after the blow-up?
This talk describes experimental and numerical investigations that are devised to provide helpful intuitions to mathematicians regarding these two questions. In particular, I will show how to detect and characterize areas of “lesser regularity” and how to connect them with possible loss of unicity.