Thursday, February 11, 2021 - 12:30 in ZOOM - Video Conference
Introduction to Convex Integration, Part I
A talk in the Cluster Group Stochastic Analysis series by
Marco Rehmeier from Bielefeld, Andre Schenke from Bielefeld
| Abstract: |
In the past decade the method of convex integration has attracted considerable attention as a means to construct weak solutions to prominent equations in fluid dynamics with "wild" energy profiles. The observation that existence of such wild solutions inevitably yields non-uniqueness results most prominently led to the celebrated resolution of Onsager’s conjecture (2018) and a proof of non-uniqueness for the 3D Navier-Stokes equations (2018).
We give a concise introduction to the theory of convex integration, tracing the analytic and geometric developments back to its roots. In particular, we discuss:
1. Nash’s (1954) seminal proof of $C^1$ embeddings, which paved the way towards modern results.
2. De Lellis and Szekelyhidi’s (2013) construction of Hölder continuous dissipative solutions to the Euler equations as a cornerstone within the race towards Onsager’s conjecture.
Finally, we will give a brief overview over convex integration in the realm of stochastically perturbed equations, including our current project.
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
|
Back
