Invariance of the Gibbs Measure for the Schrodinger-Benjamin-Ono System

Details Invariance of the Gibbs Measure for the Schrodinger-Benjamin-Ono System Invariance of the Gibbs Measure for the Schrodinger-Benjamin-Ono System

2009-04-19

arxiv.org/abs/0904.2817v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

We prove the invariance of the Gibbs measure for the periodic Schrodinger-Benjamin-Ono system (when the coupling parameter |\gamma| \ne 0, 1) by establishing a new local well-posedness in a modified Sobolev space and constructing the Gibbs measure (which is in the sub-L^2 setting for the Benjamin-Ono part.) We also show the ill-posedness result in H^s(\mathbb{T}) \times H^{s-{1/2}}(\mathbb{T}) for s < {1/2} when |\gamma| \ne 0, 1 and for any s \in \mathbb{R} when |\gamma| =1.

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