Event

Dana Mendelson (University of Chicago)

Monday, January 21, 2019 14:00to15:00
Burnside Hall Room 1205, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

Title: Almost sure wellposedness for some nonlinear dispersive equations

Abstract: Nonlinear dispersive equations model wave propagation phenomena for many physical systems, from water waves to quantum gases. For the last few decades, research on these equations has centered around questions on the existence of solutions, their long time behavior, and the possibility of singularity formation. Fundamental progress has been made in many settings, yet in some regimes, the nonlinear interactions overwhelm the dispersion of the waves, and standard methods break down.

In recent years, probabilistic tools have been instrumental in analyzing the behavior of these equations in previously inaccessible regimes.

In this talk, I will discuss several problems concerning nonlinear wave and dispersive equations with random initial data, including the energy critical nonlinear wave and Schroedinger equations, and derivative nonlinear wave equations. I will present several almost sure well-posedness and scattering results for these equations and contrast the ways in which random data techniques can be exploited in these different contexts.

 

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