On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schrödinger equations

Abstract

Under certain regularity conditions, we establish quasi-invariance of Gaussian measures on periodic functions under the flow of cubic fractional nonlinear Schrödinger equations on the one-dimensional torus.

arXiv comment42 pages; typos corrected, added Remark 1.8. To appear in Ann. Inst. H. Poincaré Anal. Non Linéaire

References in corpus (7)

• On the continuum limit for discrete NLS with long-range lattice interactions
• Blow-Up for Nonlinear Wave Equations describing Boson Stars
• Nondispersive solutions to the L2-critical half-wave equation
• Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions
• Solving the 4NLS with white noise initial data
• Transport of gaussian measures by the flow of the nonlinear Schrödinger equation
• Existence and Uniqueness theory for the fractional Schrödinger equation on the torus

Cited by in corpus (9)

• Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions
• Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces
• Quasi-Invariance of Gaussian Measures Transported by the Cubic NLS with Third-Order Dispersion on $\mathbf{T}$
• Modified energies for the periodic generalized KdV equation and applications
• Transport of low regularity Gaussian measures for the 1d quintic nonlinear Schrödinger equation
• Sharp quasi-invariance threshold for the cubic Szegő equation
• Gibbs measure dynamics for the fractional NLS
• Quantitative quasi-invariance of Gaussian measures below the energy level for the 1D generalized nonlinear Schrödinger equation and application to global well-posedness
• Quasi-Invariance under Flows Generated by Non-Linear PDEs