Projects per year
We study the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schrödinger equation on the circle. In particular, we establish an optimal regularity result for quasi-invariance of the mean-zero Gaussian measures on Sobolev spaces. The main new ingredient is an improved energy estimate established by performing an infinite iteration of normal form reductions on the energy functional. Furthermore, we show that the dispersion is essential for such a quasi-invariance result by proving non quasi-invariance of the Gaussian measures under the dynamics of the dispersionless model.
|Number of pages||49|
|Journal||Journal de l’École polytechnique — Mathématiques (JEP)|
|Publication status||Published - 30 Oct 2018|
- fourth order nonlinear Schrödinger equation
- biharmonic nonlinear Schrödinger equation
- quasi-invariant measure
- normal form method
FingerprintDive into the research topics of 'An optimal regularity result on the quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation'. Together they form a unique fingerprint.
- 1 Finished
ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
- School of Mathematics - Personal Chair of Dispersive Equations
Person: Academic: Research Active