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Abstract
In this paper, we consider the cubic nonlinear Schrödinger equation with third order dispersion on the circle. In the non-resonant case, we prove that the mean-zero Gaussian measures on Sobolev spaces H^s(핋), s>3/4, are quasi-invariant under the flow. In establishing the result, we apply gauge transformations to remove the resonant part of the dynamics and use invariance of the Gaussian measures under these gauge transformations.
Original language | English |
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Pages (from-to) | 366-381 |
Number of pages | 16 |
Journal | Comptes Rendus Mathématique |
Volume | 357 |
Issue number | 4 |
DOIs | |
Publication status | Published - 23 Apr 2019 |
Keywords / Materials (for Non-textual outputs)
- third order nonlinear Schrödinger equation
- Gaussian measure
- quasi-invariance
- non-resonance
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Dive into the research topics of 'Quasi-invariant Gaussian measures for the cubic nonlinear Schrödinger equation with third order dispersion'. Together they form a unique fingerprint.Projects
- 1 Finished
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ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
Project: Research