Averaging along irregular curves for scalar conservation laws
schedule le vendredi 07 mai 2021 de 11h00 à 12h00
Organisé par : Quentin Berger, Nathanaël Enriquez, Thierry Lévy et Shen Lin
Intervenant : Florian Bechtold (LPSM)
Lieu : Zoom
Sujet : Averaging along irregular curves for scalar conservation laws
In this talk, we study a regularization by noise phenomena for scalar conservation laws and transport equations with initial conditions of low regularity. The main tool employed will be a recent approach by Harang and Perkowski to non-linear Young integration based on quantitative regularity estimates for the local times of locally non-deterministic processes. In the particular case of fractional Brownian motion in one dimension, this permits to formulate a quantitative condition on the Hurst parameter under which well posedness to the corresponding averaged transport equation and scalar conservation law can be established globally in time.
This is based on a joint ongoing work with Nicolas Perkowski (FU Berlin)