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Session S22 - Deterministic and probabilistic aspects of nonlinear evolution equations

Wednesday, July 14, 17:45 ~ 18:15 UTC-3

Global well-posedness for the fractional NLS on the unit disk

Xueying Yu

Massachusetts Institute of Technology, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we discuss the cubic nonlinear Schr\"odinger equation with the fractional Laplacian on the unit disk. We show the global well-posedness for certain radial initial data below the energy space and establish a polynomial bound of the global solution. The result is proved by extending the I-method in the fractional nonlinear Schr\"odinger equation setting.

Joint work with Mouhamadou Sy (University of Virginia).

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