Applied Math Colloquium: Dallas Albritton (Princeton)

Title: Instability and non-uniqueness in the partial differential equations of fluid dynamics

Abstract: Over the past decade, mathematical fluid dynamics has seen remarkable progress in an unexpected direction: non-uniqueness of solutions to the fundamental partial differential equations of incompressible fluid dynamics, namely, the Euler and Navier-Stokes equations. In this colloquium, we will explain the state-of-the-art in this direction, with a particular focus on the relationship between instability and non-uniqueness. We will survey parallel programs of Jia-Svěrák-Guillod, Vishik, Bressan-Murray-Shen, and A.-Brué-Colombo, including our proof that Leray-Hopf solutions of the forced Navier-Stokes equations are not unique. Time permitting, we will discuss connections with the physics which are not yet fully understood.