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Introduction to the method of space-time resonances
Student-Run Analysis & PDE| Speaker: | Jingyang Shu, UC Davis |
| Related Webpage: | https://www.math.ucdavis.edu/~shu/ |
| Location: | 1147 MSB |
| Start time: | Thu, Jan 23 2020, 1:10PM |
The method of space-time resonances is a useful tool to investigate global existence for nonlinear dispersive equations posed in the whole space and with small initial data. This method is introduced by Germain, Masmoudi, and Shatah (Int. Math. Res. Not. (2009), 414–432). In this talk, we will take a cubically nonlinear approximate SQG front equation as an example to demonstrate the ideas of Klainerman vector field, the method of space-time resonances, and oscillatory integral estimates. The only prerequisites are integration-by-parts and the Fourier transform.