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This lecture, part 3 of 4 in a series by Daniel Tataru from UC Berkeley, explores global solutions for nonlinear dispersive waves. Delve into the fascinating interplay between linear dispersive flows—where waves with different frequencies travel at different group velocities causing dispersive decay—and nonlinear effects that allow wave interactions. The presentation introduces new conjectures describing global well-posedness and dispersive properties of solutions in challenging scenarios where nonlinear effects dominate, even with small initial data. Learn about recent breakthrough results achieved through collaboration with Mihaela Ifrim from the University of Wisconsin, Madison. This 1 hour and 54 minute scientific presentation from Institut des Hautes Etudes Scientifiques (IHES) covers important physical models and advances in understanding complex wave behaviors.
