Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions

We prove quasi-invariance of Gaussian measures supported on Sobolev spaces under the dynamics three-dimensional defocusing cubic nonlinear wave equation. As in previous work two-dimensional case, we employ a simultaneous renormalization energy functional and its time derivative. Two new ingredients case are (i) construction weighted measures, based variational formula for partition function inspired by Barashkov Gubinelli (2018), (ii) an improved argument controlling growth truncated where combine deterministic bound solutions with stochastic estimates random distributions.