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報告承辦單位: 數學與統計學院

報告題目:  Concerning ill-posedness for semilinear wave equations

報告內容:  In this talk, we investigate the problem of optimal regularity for derivative semilinear wave equations to be locally well-posed in $H^{s}$ with spatial dimension $n \leq 5$. We show this equation, with power $2\le p\le 1+4/(n-1)$, is (strongly) ill-posed in $H^{s}$ with $s = (n+5)/4$ in general. Moreover, when the nonlinearity is quadratic we establish a characterization of the structure of nonlinear terms in terms of the regularity. As a byproduct, we give an alternative proof of the failure of the local in time endpoint scale-invariant $L_{t}^{4/(n-1)}L_{x}^{\infty}$

Strichartz estimates. Finally, as an application, we also prove ill-posed results for some semilinear half wave equations. This work is joint with Chengbo Wang.

報告人姓名: 劉夢云

報告人所在單位: 浙江理工大學

報告人職稱/職務及學術頭銜: 講師

報告時間:  2021年3月30日（ 周二）上午10：00-11：00

報告方式:  騰訊會議 ID：844 753 679

報告人簡介: 劉夢云，現任浙江理工大學講師，浙江大學博士畢業，主要從事非線性波動方程理論工作的研究。包括解的長時間存在性、有限時間破裂以及解的生命跨度估計等。其研究成果發表在CVPDE、JDE、DCDS等國內外知名學術期刊上。