Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces
arXiv:2012.06732
Abstract
We continue the study on the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schrödinger equation. By considering the renormalized equation, we extend the quasi-invariance results in [30, 27] to Sobolev spaces of negative regularity. Our proof combines the approach introduced by Planchon, Tzvetkov, and Visciglia [35] with the normal form approach in [30, 27].
arXiv comment40 pages. Updated references
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