Quasi-invariant gaussian measures for one dimensional Hamiltonian PDE's

TL;DR

This paper demonstrates that Gaussian measures supported on functions with increasing Sobolev regularity remain quasi-invariant under the flow of certain one-dimensional Hamiltonian PDEs, including the regularized long wave equation.

Contribution

It establishes the quasi-invariance of Gaussian measures for specific Hamiltonian PDEs, extending understanding of measure behavior under PDE flows.

Findings

Gaussian measures are quasi-invariant under the BBM equation flow.

Supports functions with increasing Sobolev regularity.

Provides new insights into measure dynamics for Hamiltonian PDEs.

Abstract

We prove the quasi-invariance of gaussian measures (supported by functions of increasing Sobolev regularity) under the flow of one dimensional Hamiltonian PDE's such as the regularized long wave (BBM) equation.