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Summer School 2024 - Low dimensional Topology
42 videos

Summer School 2024 - Low dimensional Topology

Summer School 2023 - New trends in mathematical fluid dynamics
31 videos

Summer School 2023 - New trends in mathematical fluid dynamics

Emergent phenomena in many-body quantum systems / Phénomènes émergents des systèmes quantiques a plusieurs corps
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Emergent phenomena in many-body quantum systems / Phénomènes émergents des systèmes quantiques a plusieurs corps

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4 videos

History of mathematics, Philosophy of mathematics, and mathematics: which interactions? / Histoire des mathématiques, Philosophie des mathématiques, et mathématiques: quelles interactions?

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Summer School 2023 - New trends in mathematical fluid dynamics

Collection Summer School 2023 - New trends in mathematical fluid dynamics

Organizer(s) Scientific Committee: Anne-Laure Dalibard, Isabelle Gallagher and Frédéric Rousset / Organizing Committee: Thierry Gallay, David Gérard-Varet, Christophe Lacave, David Lannes and Evelyne Miot
Date(s) 05/06/2023 - 16/06/2023
linked URL https://if-summer2023.sciencesconf.org/
00:00:00 / 00:00:00
12 31

Instability and non-uniqueness for the Euler and Navier-Stokes equations 1

By Maria Colombo

We start introducing some basic facts about the Navier-Stokes equations, such as weak solutions, Leray global solutions, forward and backward self-similar solutions. We then explore recent developments in understanding the fundamental question of whether Leray-Hopf solutions to Navier-Stokes equations are unique. Following Jia-Sverak and Guillod-Sverak program, we describe how non-uniqueness can follow from instability in self-similarity variables. We then discuss a recent work in collaboration with Albritton and Brue’, where two distinct Leray solutions with zero initial velocity and identical body force are built. This nonuniqueness result builds in turn on Vishik's answer to another long-standing uniqueness problem about the 2D Euler equations.

Information about the video

  • Date of recording 08/06/2023
  • Date of publication 09/12/2025
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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