We prove the existence and uniqueness of a strong solution of the stochastic quantization equation in dimension 2 for almost all initial data with respect to the invariant measure. The method is based on a fixed point result in suitable Besov spaces.
"Strong solutions to the stochastic quantization equations." Ann. Probab. 31 (4) 1900 - 1916, October 2003. https://doi.org/10.1214/aop/1068646370