Next Monday July 10, 2023:

Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: Large Data Solutions to 1-D Hyperbolic Systems, Ill-Posedness, and Convex Integration
Speaker: Dr. Sam Krupa
Affiliation: Max Planck Institute for Mathematics in the Sciences (Leipzig)

Abstract. For hyperbolic systems of conservation laws in one space dimension endowed with a single convex entropy, it is an open question if it is possible to construct solutions via convex integration. Such solutions, if they exist, would be highly non-unique and exhibit little regularity. In particular, they would not have the strong traces necessary for the nonperturbative L^2 stability theory of Vasseur. Whether convex integration is possible is a question about large data, and the global geometric structure of genuine nonlinearity for the underlying PDE. In this talk, I will discuss recent work which shows the impossibility, for a large class of 2×2 systems, of doing convex integration via the use of T_4 configurations. Our work applies to every well-known 2×2 hyperbolic system of conservation laws which verifies the Liu entropy condition. This talk is based on joint work with László Székelyhidi.

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