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Invariant measures for some Hamiltonian PDEs

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If you have a question about this talk, please contact Jonathan Ben-Artzi.

In this talk, we discuss ideas and results related to invariant Gibbs measures and white noise for some Hamiltonian PDEs. First, we briefly discuss the construction of Gibb measures, and then review Bourgain’s idea for extending local-in-time solutions to global ones almost surely with respect to such Gibbs measures. The main idea is to use invariance of finite dimensional Gibbs measures as a replacement of conservation laws. In the second part, we will describe almost sure local and global well-posedness of 1-d (Wick ordered) cubic NLS below L^2. This can be viewed as a first step toward proving invariance of the white noise.

This talk is part of the Partial Differential Equations seminar series.

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