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

Speaker: 吕勇 教授，南京大学

Inviter: 黄飞敏 研究员

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

Language: Chinese

Time & Venue: 2026.8.17 16:00-17:00 N620

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.