Ill-posedness for Compressible Elastic Waves and Ideal MHD Systems
发布时间：2026年09月17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 2026-09-28 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）77201室
Both elastic waves and ideal MHD systems are physical systems with multiple wave propagation speeds. Inspired by the works of Christodoulou, we generalize Lindblad's ill-posedness results on scalar wave equation to the wave systems. We prove that the ill-posedness is caused by instantaneous shock formation, which characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in ideal MHD, we also provide a desired ill-posedness result for the compressible Euler equations, and the regularity is sharp with respect to the local well-posedness of the fluid velocity. Our proofs are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose these non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them we give a complete description of solutions' dynamics up to the earliest singular event, when a shock forms.
