Low-regularity ill-posedness of Non-strictly Hyperbolic Systems
发布时间：2026年06月02日
浏览次数：8
发布者: He Liu
主讲人： 尹思露（杭州师范大学）
活动时间： 从 2026-06-12 16:00 到 17:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）78301室
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.
