Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589826 | Journal of Functional Analysis | 2015 | 54 Pages |
Abstract
In this paper, we build a Gibbs measure for the cubic defocusing Schrödinger equation on the real line with a decreasing interaction potential, in the sense that the non-linearity |u|2u|u|2u is multiplied by a function χ which we assume integrable and smooth enough. We prove that this equation is globally well-posed in the support of this measure and that the measure is invariant under the flow of the equation. What is more, the support of the measure (the set of initial data) is disjoint from L2L2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Federico Cacciafesta, Anne-Sophie de Suzzoni,