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Local well-posedness of the kinetic derivative nonlinear Schroedinger equation on 1D torus for small initial data


開催時期 2020-01-17 15:30~2020-01-17 17:00

場所 福岡大学・セミナーハウス・2階セミナー室D

受講対象  

講師 堤 誉志雄 (京都大学)

【概要】
I talk about the local well-posedness of the Cauchy problem for the kinetic derivative nonlinear Schroedinger equation (for short, KDNLS) on 1D torus under the smallness assumption on initial data. KDNLS takes the resonant interaction between the wave modulation and the ions into account, while it is ignored in DNLS. The word "kinetic'' implies that the collective motion of ions in a plasma is modeled by the Vlasov equation and not by the fluid equation. From a viewpoint of the Fourier restriction norm method, the "high×low to high" interaction causes a problem. For DNLS, the gauge transformation removes this interaction, but for KDNLS, it does not work well. But from a physical point of view, the dissipative effect is expected from KDNLS. I explain how to use this dissipative nature of KDNLS for the proof of local well-posedness under the smallness assumption on initial data. I also present the uniqueness of solution without the smallness of initial data.
This is a joint work with Nobu Kishimoto, RIMS, Kyoto University.


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