**The**** speaker:** Professor Eduard Feireisl (Institute of Mathematics of the Academy of Sciences of the Czech Republic; Institute of Mathematics, Technische Universitat Berlin)

**Title of the talk:**“Obstacle problem, Euler system, and turbulence”.

**Time:** Thursday, 6 of May 2021, 16:00 - 17:00.

**Abstract**. We consider a statistical limit of solutions to the compressible Navier-Stokes system in the high Reynolds number regime in a domain exterior to a rigid body. We investigate to what extent this highly turbulent regime can be modeled by an external stochastic perturbation, as suggested in the related physics literature. To this end, we interpret the statistical limit as a stochastic process on the associated trajectory space. We suppose that the limit process is statistically equivalent to a solution of thestochastic compressible Euler system. Then, necessarily,

(a) the stochastic forcing is not active - the limit is a statistical solution of the deterministic Euler system;

(b) the solutions S-converge to the limit;

(c) if, in addition, the expected value of the limit process solves the Euler system, then the limit is deterministic and the convergence is strong in the L^p-sense.

These results strongly indicate that a stochastic forcing may not be a suitable model for turbulent randomness incompressible fluid flows.

ZOOM link:

https://us02web.zoom.us/j/83673138944?pwd=azQyc1BwUjJFY3VjMStLbFR5Z2VwUT09

ZOOM Id: 836 7313 8944

Passcode: 808818

We are pleased to inform you that the information on previous talks is available on the seminar web page https://researchseminars.org/seminar/Cafe_Analysis_and_Fluid see Past Talks section.

** Organizing Committee:** Professors Zhen Lei, Mikhail Korobkov, Adele Ferone, Remigio Russo and Konstantin Pileckas.

This seminar is organized by Fudan University (Shanghai, China) with the collaboration of Universita degli studi della Campania "Luigi Vanvitelli" (Caserta, Italy) and Vilnius University (Vilnius, Lithuania). This seminar is meant to gather renowned experts working on Geometric and Real Analysis with applications to PDEs and Mathematical Physics and represents an opportunity for presenting high-impact research, as well as facilitating the exchange of ideas between researchers.