Random Data Final-State Problem for the Mass-Subcritical NLS in L²

Author

Jason Murphy, Missouri University of Science and TechnologyFollow

Abstract

We study the final-state problem for the mass-subcritical NLS above the Strauss exponent. For u₊ ∈ L² , we perform a physical-space randomization, yielding random final states (formula presented). We show that for almost every ω, there exists a unique, global solution to NLS that scatters to (formula presented). This complements the deterministic result of Nakanishi, which proved the existence (but not necessarily uniqueness) of solutions scattering to prescribed L² final states.

Recommended Citation

J. Murphy, "Random Data Final-State Problem for the Mass-Subcritical NLS in L²," Proceedings of the American Mathematical Society, vol. 147, no. 1, pp. 339 - 350, American Mathematical Society, Jan 2019.

The definitive version is available at https://doi.org/10.1090/proc/14275

Department(s)

Mathematics and Statistics

Comments

The author was supported by the NSF Postdoctoral Fellowship DMS-1400706 at the University of California, Berkeley.

International Standard Serial Number (ISSN)

0002-9939; 1088-6826

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 2019