Gibbs measure evolution in radial nonlinear wave and Schr\"odinger equations on the ball

Jean Bourgain; Aynur Bulut

Gibbs measure evolution in radial nonlinear wave and Schr\"odinger equations on the ball

Analysis of PDEs 2015-08-12 v1

Authors: Jean Bourgain , Aynur Bulut

Abstract

We establish new results for the radial nonlinear wave and Schr\"odinger equations on the ball in $\Bbb R^2$ and $\Bbb R^3$ , for random initial data. More precisely, a well-defined and unique dynamics is obtained on the support of the corresponding Gibbs measure. This complements results from \cite{B-T1,B-T2} and \cite {T1,T2}.

Keywords

Gibbs measure radial nonlinear wave equation nonlinear Schrödinger equation ball domain random initial data well-defined dynamics

Cite

@article{arxiv.1205.1187,
  title  = {Gibbs measure evolution in radial nonlinear wave and Schr\"odinger equations on the ball},
  author = {Jean Bourgain and Aynur Bulut},
  journal= {arXiv preprint arXiv:1205.1187},
  year   = {2015}
}

Comments

Research announcement, 6 pages

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