Irregular solutions of the transport and Navier-Stokes equations

The understanding of irregular solutions in fluid dynamics is a formidable challenge in the analysis of PDEs and has intriguing connections with the description of turbulent phenomena. For the transport equation, a PDE whose analysis lies at the basis of nonlinear PDEs such as Euler and Navier-Stokes, this entangles with a suitable notion of flow of the ODE associated to a nonsmooth vector field. I will introduce the topic, describe some of the main challenges of the theory related to uniqueness issues and present a versatile method for the construction of irregular solutions, together with its consequences.

Passcode (if needed): 827479
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