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June 2022

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[Indico] Elia Bruè, Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, 28/06/2022, 16:30 Europe/Rome
by maria.stella.gelli＠unipi.it 23 Jun '22

23 Jun '22

Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, Speaker(s): Elia Bruè, Institute for Advanced Study (Princeton), Date and time: 28 Jun 2022, 16:30 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/100 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. -- Indico :: Email Notifier https://events.dm.unipi.it/e/100

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