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Almost sure scattering for the energy-critical nonlinear wave equation

Banff International Research Station for Mathematical Innovation and Discovery

We discuss the defocusing energy-critical nonlinear wave equation in four dimensions. For deterministic and smooth initial data, solutions exist globally and scatter. In contrast, since deterministic and rough initial data can lead to norm inflation, the energy-critical NLW is ill-posed at low regularities. In this talk, we show that the global existence and scattering behavior persists under random and rough perturbations of the initial data. In particular, norm inflation only occurs for exceptional sets of rough initial data. As part of the argument, we discuss techniques from restriction theory, such as wave packet decompositions and Bourgain's bush argument.

Mathematics; Partial differential equations; Fourier analysis

video/mp4

Author affiliation: University of California, Los Angeles

2019-12-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73027

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/