University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Resonances, genericity and rational normal forms: The KillBill theory

Resonances, genericity and rational normal forms: The KillBill theory

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If you have a question about this talk, please contact pierre raphael.

Normal form theory has been succesfully used to analyze the long time behavior of semi-linear PDEs on compact manifold. I will recall some classical results and show how the presence of nonlinear resonances drives the stability of solutions for long times, for smooth and small initial data. I will then discuss two results: the case of waves equation in high dimension, and the completely resonant Schrödinger equation in 1D for which we can prove long time stability for « generic » initial data in Sobolev space. This last result requires the use of rationnal normal forms conjugating the dynamics to an almost integrable one on some open set avoiding resonances. These are joint works with Joackim Bernier and Benoît Grébert.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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