Projects per year
Abstract / Description of output
We consider the defocusing nonlinear Schrödinger equations on the two-dimensional compact Riemannian manifold without boundary or a bounded domain in ℝ^2. In particular, we discuss the Wick renormalization in terms of the Hermite polynomials and the Laguerre polynomials and construct the Gibbs measures corresponding to the Wick ordered Hamiltonian. Then, we construct global-in-time solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure.
Original language | English |
---|---|
Pages (from-to) | 397-445 |
Number of pages | 49 |
Journal | Stochastics and Partial Differential Equations: Analysis and Computations |
Volume | 6 |
Issue number | 3 |
Early online date | 26 Mar 2018 |
DOIs | |
Publication status | Published - Sept 2018 |
Keywords / Materials (for Non-textual outputs)
- nonlinear Schrödinger equation
- Gibbs measure
- Wick ordering
- Hermite polynomial
- Laguerre polynomial
- white noise functional
Fingerprint
Dive into the research topics of 'A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations'. Together they form a unique fingerprint.Projects
- 1 Finished
-
ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
Project: Research