Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Random data final-state problem for the mass-subcritical NLS in $L^2$
HTML articles powered by AMS MathViewer

by Jason Murphy PDF
Proc. Amer. Math. Soc. 147 (2019), 339-350 Request permission

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
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
  • MR Author ID: 1034475
  • Email: jason.murphy@mst.edu
  • 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
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 339-350
  • MSC (2010): Primary 35Q55
  • DOI: https://doi.org/10.1090/proc/14275
  • MathSciNet review: 3876753