Initial value problems for nonlinear dispersive equations at critical regularity
Sebastian HerrUniversität Bielefeld, Germany
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Global regularity results for nonlinear dispersive equations hinge on a thorough understanding of the Cauchy problem in spaces of functions of low regularity. This is most challenging in scale invariant regimes as solutions interact strongly on multiple frequency-scales. Here, some recent progress on the critical well-posedness theory will be reviewed, with a focus on nonlinear Schrödinger and Dirac equations.