报告人: 吴奕飞  教授

报告时间：4月11日上午11点

单 位: 天津大学

摘 要: Abstract: In this talk, we discuss the instability of the solitary wave solutions for some dispersive equations.

First, we consider the nonlinear Klein-Gordon equation. It has the standing wave solutions $u_\omega=e^{i\omega t}\phi_{\omega}$ in the L2-subcritical case, with the frequency $\omega\in(-1,1)$. It was proved by Shatah (1983), Shatah, Strauss (1985), and Ohta, Todorova (2007) that there exists a critical frequency $\omega_c\in (0,1)$ such that the standing waves solution $u_\omega$ is orbitally stable when $\omega_c<|\omega|<1$, orbitally unstable when $|\omega|<\omega_c$, and orbitally unstable when $|\omega|=\omega_c$ and $d\ge 2$. The one dimension problem was left after then. In this talk, we give the proof of this remained problem.

Second, we discuss the extension of the argument to the general dispersive equations. In particular, we study the instability of the solitary wave solutions for a class of the dispersive equations in the degenerate case, without

any restriction on the regularity of the nonlinearity.

As an application, we consider the generalized derivative Schr\"odinger equation, for which the solitary wave solution in the degenerated case was proved previously by Fukaya (2016) to be orbitally instable when the power $\sigma \in [\frac76, 2)$. Now we can cover the whole region of $\sigma\in (0,1)$. This is a jointed work with Zihua Guo, and Cui Ning. The argument was also used to the generalized Boussinesq equations, which was from a jointed work with Li, Ohta and Xue.

报告人简介：

吴奕飞,天津大学教授,博士生导师, 曾获得广东省优秀博士论文,全国百篇优秀博士论文提名. 研究方向是偏微分方程和调和分析.在国际一流期刊Journal of the European Mathematical Society, International Mathematics Research Notices, Advances in Mathematics, Analysis & PDE, SIAM Journal of Mathematical Analysis, Journal of Differential Equation等发表20多篇论文. 多次受邀到法国,韩国,澳大利亚访问或做学术报告。