Low-regularity ill-posedness of Non-strictly Hyperbolic Systems
Time: 2026-06-02
Published By: He Liu
Speaker(s): Silu Yin (Hangzhou Normal University)
Time: 16:00-17:00 June 12, 2026
Venue: Room 78301, Jingchunyuan 78, BICMR
In this talk, we investigate the ill-posedness of several non-strictly hyperbolic systems characterized by multiple propagation speeds, encompassing elastodynamic waves, the compressible ideal MHD system, and Euler equations. For scalar quasilinear wave equation, the local well-posedness in $H^s(R^n)\times H^{s-1}(R^n)$ has been established, where the regularity threshold is defined as $s>3$ for $n=3$ and $s>11/4$ for $n=2$ Here, we construct explicit counterexamples to demonstrate the failure of local existence for low-regularity solutions to the aforementioned physical systems at the critical borderline regularity. Our proof is based on a coalition of a carefully designed algebraic approach with Christodoulou’s geometric approach. We give a detailed description of solution dynamics up to the earliest singular event, when a shock forms. This talk is based on joint works with Xinliang An and Haoyang Chen.
