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

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.

References in corpus (3)

• Invariance of the white noise for KdV
• Long time dynamics for the one dimensional non linear Schrödinger equation
• Two Dimensional NLS Equation With Random Radial Data

Cited by in corpus (7)

• Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions
• Transport of gaussian measures by the flow of the nonlinear Schrödinger equation
• Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces
• Quasi-invariance of fractional Gaussian fields nonlinear wave equation with polynomial nonlinearity
• Modified energies for the periodic generalized KdV equation and applications
• Almost sure global well posedness for the BBM equation with infinite $L^2$ initial data
• Probabilistic preservation of regularity for periodic nonlinear Schrödinger equations