Global well-posedness for the derivative nonlinear Schrödinger equation on the torus

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• Razvan Mosincat, University of Edinburgh
• Monday 31 October 2016, 16:00-17:00
• Lecture Theatre 1, Strathcona Building.

If you have a question about this talk, please contact Andrew Morris.

In this talk, we will discuss the global well-posedness problem for the derivative nonlinear Schr\”odinger equation on the torus. We will first review some of the features of this equation (e.g. conservation laws and gauge transformations) as well as previous results relevant to our discussion (e.g. the local well-posedness result via the Fourier restriction norm method). We prove global well-posedness by employing the $I$-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao. In order to treat low regularity solutions, we use resonant decomposition. Finally, we will see how one can make use of the momentum conservation law and incorporate it into this apparatus to improve the mass threshold for global-in-time solutions.

This talk is part of the Analysis Seminar series.

This talk is included in these lists:

• Analysis Seminar
• Lecture Theatre 1, Strathcona Building
• School of Mathematics Events

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