報告承辦單位: 數(shù)學與統(tǒng)計學院

報告題目:   Low regularity ill-posedness for ideal compressible MHD in 3D and 2D

報告內容: 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.報告人姓名:  尹思露

報告人所在單位: 杭州師范大學

報告人職稱/職務及學術頭銜:  副教授

報告時間:  2022.11.08  10:00-12:00

報告方式: 騰訊會議 會議 ID：494-367-118

報告人簡介: 尹思露，杭州師范大學副教授。博士畢業(yè)于復旦大學，期間到美國匹茲堡大學聯(lián)合培養(yǎng)一年。主持了國家自然科學基金青年科學基金、浙江省自然科學基金青年項目、上海市科委青年科技英才揚帆計劃、中國博士后科學基金面上項目。其成果發(fā)表在著名雜志AJM、SIAM、JDE等。