宁波大学

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甬江数学讲坛116讲(2020年第43讲)

发布日期:2020-10-09 作者:数学与统计学院 文章来源:未知  责任编辑:

报告题目:Instability of the solitary wave solutions for some dispersive equations

报 告 人:吴奕飞 (天津大学 教授)

会议时间:20201014  16:00开始

会议链接:https://meeting.tencent.com/s/TFxekQzRSFXA

会议 ID539 138 335

报告摘要: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 generalized derivative Schrodinger equation. In particular, we study the instability of the solitary wave solutions in the degenerate case, without any restriction on the regularity of the nonlinearity. Previously, the solitary wave solution in the degenerated case was proved 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. Lastly, we also discuss the application of this argument to the generalized Boussinesq equations, which was from a jointed work with Li, Ohta and Xue.

报告人介绍:吴奕飞,天津大学应用数学中心教授,博士生导师,国家万人计划青年拔尖人才,主要从事基础数学偏微分方程方面的研究工作,在J. Eur. Math. Soc(JEMS)Adv. MathAnalysis & PDEInter. Math. Res. Notice等国际著名学术期刊发表20余篇论文,主持多项国家自然科学基金项目、曾获全国优秀博士论文提名奖。


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