Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Random data final-state problem for the mass-subcritical NLS in $ L^2$


Author: Jason Murphy
Journal: Proc. Amer. Math. Soc. 147 (2019), 339-350
MSC (2010): Primary 35Q55
DOI: https://doi.org/10.1090/proc/14275
Published electronically: October 18, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the final-state problem for the mass-subcritical NLS above the Strauss exponent. For $ u_+\in L^2$, we perform a physical-space randomization, yielding random final states $ u_+^\omega \in L^2$. We show that for almost every $ \omega $, there exists a unique, global solution to NLS that scatters to $ u_+^\omega $. This complements the deterministic result of Nakanishi, which proved the existence (but not necessarily uniqueness) of solutions scattering to prescribed $ L^2$ final states.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35Q55

Retrieve articles in all journals with MSC (2010): 35Q55


Additional Information

Jason Murphy
Affiliation: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Missouri 65409
Email: jason.murphy@mst.edu

DOI: https://doi.org/10.1090/proc/14275
Received by editor(s): February 23, 2018
Received by editor(s) in revised form: June 7, 2018
Published electronically: October 18, 2018
Additional Notes: The author was supported by the NSF Postdoctoral Fellowship DMS-1400706 at the University of California, Berkeley.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2018 American Mathematical Society