报告承办单位: 数学与统计学院

报告题目:   Low regularity ill-posedness for ideal compressible MHD in 3D and 2D

报告内容: In this talk, we construct counterexamples to the local existence of low-regularity solutions to the ideal MHD system in three and two spatial dimensions (3D and 2D). For 3D, inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for MHD system are ill-posed in $H^2$. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. For the 2D case, we construct the counterexamples to local well-posedness in $H^{7/4}$. This talk is based on joint works with Xinliang An and Haoyang Chen.报告人姓名:  尹思露

报告人所在单位: 杭州师范大学

报告人职称/职务及学术头衔:  副教授

报告时间:  2022.11.08  10:00-12:00

报告方式: 腾讯会议 会议 ID：494-367-118

报告人简介: 尹思露，杭州师范大学副教授。博士毕业于复旦大学，期间到美国匹兹堡大学联合培养一年。主持了国家自然科学基金青年科学基金、浙江省自然科学基金青年项目、上海市科委青年科技英才扬帆计划、中国博士后科学基金面上项目。其成果发表在著名杂志AJM、SIAM、JDE等。