The dynamical sine-Gordon model in the full subcritical regime

Understand

We prove that the dynamical sine-Gordon equation on the two dimensional torus introduced in [HS16] is locally well-posed for the entire subcritical regime.

• At first glance this equation is far out of the scope of the local existence theory available in the framework of regularity structures [Hai14, BHZ16, CH16, BCCH17] since it involves a non-polynomial nonlinearity and the solution is expected to be a distribution (without any additional small parameter as in [FG17, HX18]).
• In [HS16] this was overcome by a change of variable, but the new equation that arises has a multiplicative dependence on highly non-Gaussian noises which makes stochastic estimates highly non-trivial - as a result [HS16] was only able to treat part of the subcritical regime.
• Moreover, the cumulants of these noises fall out of the scope of the later work [CH16].