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Theory of regularity structures and dynamical Sine-Gordon model

  • Hao Shen (University of Warwick)
A3 01 (Sophus-Lie room)

Abstract

We discuss the dynamical sine-Gordon equation in two space dimension with parameter $\beta$. Our main result is that when $\beta^2 < 16\pi /3$, the Wick renormalised equation is locally well-posed. We aim to use this particular equation as an example to illustrate the general ideas in the theory of regularity structures recently developed by Martin Hairer.

A main feature of this model is that when $\beta^2 < 4\pi$, previous solution theory applies, while for $\beta^2 \in [4\pi, 16\pi /3)$, one has to apply the theory of regularity structures. This is joint work with Martin Hairer.

Upcoming Events of this Seminar

  • Monday, 14.07.25 tba with Alexandra Holzinger
  • Tuesday, 15.07.25 tba with Anna Shalova
  • Tuesday, 12.08.25 tba with Sarah-Jean Meyer
  • Friday, 15.08.25 tba with Thomas Suchanek
  • Friday, 22.08.25 tba with Nikolay Barashkov
  • Friday, 29.08.25 tba with Andreas Koller