Seminar In the Analysis and Methods of PDE (SIAM PDE): Vlad Vicol

Date: November 5, 2020

Speaker: Vlad Vicol, Courant Institute of Mathematical Sciences, NYU

Title: Shock formation and vorticity creation for compressible Euler

Abstract: In this talk, I will discuss a long term project, joint with Tristan Buckmaster and Steve Shkoller, concerning the formation of singularities (shocks) for the compressible Euler equations with the ideal gas law. We provide a constructive proof of stable shock formation from smooth initial datum, of finite energy, and with no vacuum regions. Via modulated self-similar variables, the blow-up time and location can be explicitly computed, and at the blow-up time, the solutions can be shown to have precisely Holder 1/3 regularity. Additionally, for the non-isentropic problem sounds waves interact with entropy waves to produce vorticity at the shock.

Moderator: Edriss S. Titi, Texas A&M University and University of Cambridge and Weizmann Institute of Science

The COVID-19 pandemic and consequent social distancing call for online venues of research dissemination. This webinar will serve as a way to recognize achievements in our area, and it will be expected to help promoting the standing of both SIMA and APDE. Further, these webinars should be beneficial to mathematicians who are in relatively isolated places.

This webinar is intended to continue well beyond this social distancing period. Two type of webinars are planned:
(i) Colloquium-type webinars by outstanding speakers presenting a survey of results on a topic where critical progress was recently achieved (and not necessarily published in SIMA);
(ii) More focused seminar-like webinars based on some of the best articles accepted by SIMA.
More information can be found here: https://sinews.siam.org/Details-Page/...