報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: Low regularity ill-posedness for ideal compressible MHD in 3D and 2D
報(bào)告內(nèi)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(bào)告人姓名: 尹思露
報(bào)告人所在單位: 杭州師范大學(xué)
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 副教授
報(bào)告時(shí)間: 2022.11.08 10:00-12:00
報(bào)告方式: 騰訊會(huì)議 會(huì)議 ID：494-367-118
報(bào)告人簡(jiǎn)介: 尹思露，杭州師范大學(xué)副教授。博士畢業(yè)于復(fù)旦大學(xué)，期間到美國(guó)匹茲堡大學(xué)聯(lián)合培養(yǎng)一年。主持了國(guó)家自然科學(xué)基金青年科學(xué)基金、浙江省自然科學(xué)基金青年項(xiàng)目、上海市科委青年科技英才揚(yáng)帆計(jì)劃、中國(guó)博士后科學(xué)基金面上項(xiàng)目。其成果發(fā)表在著名雜志AJM、SIAM、JDE等。
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