Events for 03/16/2021 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Simon Markfelder, University of Cambridge

Title: Convex integration applied to the compressible Euler equations

Abstract: We consider the compressible Euler system in multiple space dimensions, which is a particular example of a system of hyperbolic conservation laws. Whereas for scalar conservation laws one has achieved a thorough well-posedness theory, one is able to show that there exist initial data for which the multi-dimensional compressible Euler system admits infinitely many solutions. These non-uniqueness results are based on the convex integration method, which was first used in the context of fluid dynamics by De Lellis and Szekelyhidi in order to construct solutions of the incompressible Euler equations. In this talk we give an overview over some non-uniqueness results for compressible Euler together with the basic ideas of the proofs.