SMS scnews item created by Miranda Luo at Fri 19 Aug 2022 1532
Type: Seminar
Modified: Mon 22 Aug 2022 0954
Distribution: World
Expiry: 5 Sep 2022
Calendar1: 5 Sep 2022 1700-1800
CalLoc1: Zoom webinar
Auth: miranda@w7r3b0j3.staff.wireless.sydney.edu.au (jluo0722) in SMS-SAML

# Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations

### Martina Hofmanova

Dear friends and colleagues,

on Monday, 5 September 2022 at
03:00 PM for Beijing, Hong Kong and Perth
04:00 PM for Seoul and Tokyo
05:00 PM for Canberra, Melbourne and Sydney
07:00 PM for Auckland

Professor Martina Hofmanova is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations

Abstract:

We establish existence of infinitely many stationary solutions as well as ergodic stationary solutions to the three dimensional Navier--Stokes and Euler equations in the deterministic as well as stochastic setting, driven by an additive noise. The solutions belong to the regularity class $C(\mathbb{R};H^{\vartheta})\cap C^{\vartheta}(\mathbb{R};L^{2})$ for some $\vartheta>0$ and satisfy the equations in an analytically weak sense. Moreover, we are able to make conclusions regarding the vanishing viscosity limit and anomalous dissipation. The result is based on a new stochastic version of the convex integration method which provides uniform moment bounds locally in the aforementioned function spaces.

Chair: Ben Goldys (University of Sydney)

More information and how to attend this talk can be found at the seminar webpage .

Miranda
On behalf of Daniel H. and Ben

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## Webinar Speaker

Martina Hofmanova
Professor @ University of Bielefeld, Germany

Mrs Hofmanova received her PhD in 2013 at Ecole Normale Superieure de Cachan, Antenne de Bretagne, Rennes, France. After a post-doctaral reseach position in the academic year 2013/14 at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, she was appointed as assistant lecturer from 2014-2016 at the Technical University of Berlin, Germany, where she also was promoted to Junior-Professor (2016-2017). From 2017-2018, Mrs Hofmanova accepted a temporary Professorship at the University of Bielefeld, where she was promoted to Full Professor at the end of 2018.

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