Non-uniqueness of Leray solutions of the forced Navier-Stokes equations – Elia Bruè (Institute for Advanced Study (Princeton))

Venue

Dipartimento di Matematica, Aula Magna.

Abstract

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.

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