题目：Low regularity ill-posedness for elastic waves and for MHD system

报告人：陈昊阳（南开大学数学学院）

时间：2026年6月11日，星期四 上午9:00

地点：文北206

摘要: In this talk, we investigate low-regularity ill-posedness for elastic wave equations and the ideal compressible MHD system in three and two spatial dimensions. For 3D, we generalize Lindblad’s classic results on scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed at threshold regularity $H^3$ and $H^2$, respectively. Both elastic waves and MHD are physical systems with multiple wave-speeds. We further prove that the ill-posedness is driven by shock formation, which is characterized by the vanishing of the inverse foliation density. Our proof is based on a coalition of a carefully designed algebraic approach and a geometric approach. In 2D, we prove the $H^11/4$ and $H^7/4$ ill-posedness for the elastic wave equations and ideal MHD system. Compared with the 3D case, the construction of ill-posed profile in 2D is more delicate.While in 3D, the shock formation argument is more involved due to the more complicated structures of the systems. We also report our recent works on low regularity local well-posedness for certain elastic material, and on self-similar type shock formation.  

邀请人：于品