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Space-time resonances and high-frequency Raman instabilities in the two-fluid Euler-Maxwell system

发布时间：2021-11-10 作者： 浏览次数：
Speaker: 吕勇 DateTime: 2021年11月12日（周五）下午2:30-3:30
Brief Introduction to Speaker:

吕勇，南京大学副教授。本科毕业于中国科技大学数学系，在法国巴黎七大取得硕士和博士学位，之后在布拉格查理大学从事博士后研究。吕勇的研究领域是偏微分方程的数学分析，主要在非线性几何光学以及流体力学方程两个方向。研究成果在Archive for Rational Mechanics and Analysis，Mémoires de la Société Mathématique de France，Calculus of Variations and Partial Differential Equations，SIAM: Journal on Mathematical Analysis, ESAIM: Control, Optimisation and Calculus of Variations，Journal of Differential Equations等期刊发表。

 Place: 腾讯会议ID：471 804 642
Abstract:We apply the symbolic flow method to the two-fluid Euler-Maxwell system, and show that space-time resonances induce high-frequency Raman and Langmuir instabilities. A consequence is that the Zakharov WKB approximation to Euler-Maxwell is unstable for non-zero group velocities. A key step in the proof is the reformulation of the set of resonant frequencies as the locus of weak hyperbolicity for linearized equations around the WKB solution. Due to large transverse variations in the WKB profile, the equation satisfied by the symbolic flow around resonant frequencies is a linear partial differential equation. At space-time resonances corresponding to the Raman or Langmuir instability, we observe a fast growth of the symbolic flow, which translates into an instability result for the original system.
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