Department of Mathematics

Analysis and PDE

  •  Shi-Zhuo Looi, UC Berkeley
  •  Asymptotics for odd- and even-dimensional waves
  •  09/28/2022
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Willie Wai-Yeung Wong (

In this talk, I will give a survey of recent and upcoming results on various linear, semilinear and quasilinear wave equations on a wide class of dynamical spacetimes in various even and odd spatial dimensions. These results include asymptotics for a wide range of nonlinearities. We also highlight a dichotomy in odd dimensions between stationary and nonstationary backgrounds and explain how the stationary backgrounds lead to a faster decay rate for waves. For many of these results, the spacetimes under consideration have only weak asymptotic flatness conditions and are allowed to be large perturbations of the Minkowski spacetime. We explain the dichotomy between even- and odd-dimensional wave behaviour and how we view this dichotomy as a generalisation of the contrast between the classical weak Huygens' principle and the classical strong Huygens' principle. Part of this work is joint with Mihai Tohaneanu and Jared Wunsch.



Department of Mathematics
Michigan State University
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