Theory of regularity structures and dynamical Sine-Gordon model

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.