Non-uniqueness of Leray solutions of the forced Navier-Stokes equations

by Elia Bruè (Institute for Advanced Study (Princeton))

Tuesday 28 Jun 2022, 16:30 → 17:30 Europe/Rome

Aula Magna (Dipartimento di Matematica)

In his seminal work, Leray demonstrated the existence of global weak solutions, with nonincreasing energy, to the Navier-Stokes equations in three dimensions. In this talk, we exhibit two distinct Leray solutions with zero initial velocity and identical body force.  Building on a recent work of Vishik, we construct a linear unstable self-similar solution to the 3D Navier-Stokes with force. We employ the linear instability of the latter to build the second solution, which is a trajectory on the unstable manifold, in accordance with the predictions of Jia and Šverák.