Tuesday, June 4, 2024 - 16:00 in ZiF
Hyperbolic sine-Gordon model beyond the first threshold
A talk in the Harmonic and Stochastic Analysis of Dispersive PDEs series by
Younes Zine from EPFL
| Abstract: |
Over the past two decades, significant progress has been made in understanding singular random
dispersive PDEs with polynomial nonlinearities. However, non-polynomial nonlinearities
remain poorly understood. This talk presents recent advancements in this direction, focusing
on the well-posedness of the two-dimensional damped wave equation with a sine nonlinearity,
driven by additive space-time white noise.
I will introduce the physical Fourier restriction norm method, a novel framework that tackles
the challenges of non-polynomial settings. This method leverages recent developments in the
Fourier restriction theory for the cone to establish key deterministic estimates. Additionally,
I will discuss the proof of nonlinear smoothing for the imaginary Gaussian multiplicative chaos,
the main probabilistic component of our argument, utilizing combinatorial and geometric
techniques. This is joint work with Tadahiro Oh (Edinburgh, UK).
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