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arXiv · 1804.10631

Unconditional Uniqueness Results for the Nonlinear Schr\"odinger Equation

Sebastian Herr·Vedran Sohinger
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Abstract

We study the problem of unconditional uniqueness of solutions to the cubic nonlinear Schr\"odinger equation. We introduce a new strategy to approach this problem on bounded domains, in particular on rectangular tori. It is a known fact that solutions to the cubic NLS give rise to solutions of the Gross-Pitaevskii hierarchy, which is an infinite-dimensional system of linear equations. By using the uniqueness analysis of the Gross-Pitaevskii hierarchy, we obtain new unconditional uniqueness results for the cubic NLS on rectangular tori, which cover the full scaling-subcritical regime in high dimensions. In fact, we prove a more general result which is conditional on the domain. In addition, we observe that well-posedness of the cubic NLS in Fourier-Lebesgue spaces implies unconditional uniqueness.

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Sebastian Herr, Vedran Sohinger. 2018-04-27. Unconditional Uniqueness Results for the Nonlinear Schr\"odinger Equation. https://doi.org/10.1142/s021919971850058x

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