Projects per year
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1785-1826 |
| Number of pages | 42 |
| Journal | Journal of the European Mathematical Society |
| Volume | 22 |
| Issue number | 6 |
| Early online date | 27 Feb 2020 |
| DOIs | |
| Publication status | Published - 1 Jun 2020 |
Keywords
- nonlinear wave equation
- nonlinear Klein-Gordon equation
- Gaussian measure
- quasi-invariance
Fingerprint
Dive into the research topics of 'Quasi-invariant Gaussian measures for the two-dimensional defocusing cubic nonlinear wave equation'. Together they form a unique fingerprint.Projects
- 1 Finished
-
ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
Project: Research
Profiles
-
Tadahiro Oh
- School of Mathematics - Personal Chair of Dispersive Equations
Person: Academic: Research Active