A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations

Tadahiro Oh, Laurent Thomann

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)397-445
Number of pages49
JournalStochastics and Partial Differential Equations: Analysis and Computations
Volume6
Issue number3
Early online date26 Mar 2018
DOIs
Publication statusPublished - Sept 2018

Keywords / Materials (for Non-textual outputs)

  • nonlinear Schrödinger equation
  • Gibbs measure
  • Wick ordering
  • Hermite polynomial
  • Laguerre polynomial
  • white noise functional

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