报告承办单位: 数学与统计学院

报告题目:  Concerning ill-posedness for semilinear wave equations

报告内容:  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.

报告人姓名: 刘梦云

报告人所在单位: 浙江理工大学

报告人职称/职务及学术头衔: 讲师

报告时间:  2021年3月30日（ 周二）上午10：00-11：00

报告方式:  腾讯会议 ID：844 753 679

报告人简介: 刘梦云，现任浙江理工大学讲师，浙江大学博士毕业，主要从事非线性波动方程理论工作的研究。包括解的长时间存在性、有限时间破裂以及解的生命跨度估计等。其研究成果发表在CVPDE、JDE、DCDS等国内外知名学术期刊上。