Quasi-Invariance of Gaussian Measures Transported by the Cubic NLS with Third-Order Dispersion on $\mathbf{T}$

Arnaud Debussche, Yoshio Tsutsumi

We consider the Nonlinear Schrödinger (NLS) equation and prove that the Gaussian measure with covariance $(1-{\partial }_x^2{)}^{-\alpha }$ on $L^2(\mathbf{T})$ is quasi-invariant for the asso…