Quasi-invariant Gaussian measures for the two-dimensional defocusing cubic nonlinear wave equation
Analysis of PDEs
2018-11-20 v3 Probability
Abstract
We study the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the two-dimensional defocusing cubic nonlinear wave equation (NLW). Under some regularity condition, we prove quasi-invariance of the mean-zero Gaussian measures on Sobolev spaces for the NLW dynamics. We achieve this goal by introducing a simultaneous renormalization on the energy functional and its time derivative and establishing a renormalized energy estimate in the probabilistic setting.
Keywords
Cite
@article{arxiv.1703.10718,
title = {Quasi-invariant Gaussian measures for the two-dimensional defocusing cubic nonlinear wave equation},
author = {Tadahiro Oh and Nikolay Tzvetkov},
journal= {arXiv preprint arXiv:1703.10718},
year = {2018}
}
Comments
37 pages. Minor typos corrected. To appear in J. Eur. Math. Soc