A NOTE ON DECAY PROPERTY OF NONLINEAR SCHRÖDINGER EQUATIONS

Chenjie Fan, Zehua Zhao

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this note, we show the existence of a special solution u to defocusing cubic NLS in 3d, which lives in Hs for all s > 0, but scatters to a linear solution in a very slow way. We prove for this u, for all > 0, one has supt>0 tu(t) − eitΔu+H 1/2 = ∞. Note that such a slow asymptotic convergence is impossible if one further pose the initial data of u(0) be in L1. We expect that similar construction hold the for other NLS models. It can been seen the slow convergence is caused by the fact that there are delayed backward scattering profile in the initial data, we also illustrate why L1 condition of initial data will get rid of this phenomena.

Original languageEnglish
Pages (from-to)2527-2542
Number of pages16
JournalProceedings of the American Mathematical Society
Volume151
Issue number6
DOIs
Publication statusPublished - Jun 2023

Keywords

  • Nonlinear Schrödinger equation
  • convergence rate
  • decay estimate
  • scattering
  • scattering rate

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Fan, C., & Zhao, Z. (2023). A NOTE ON DECAY PROPERTY OF NONLINEAR SCHRÖDINGER EQUATIONS. Proceedings of the American Mathematical Society, 151(6), 2527-2542. https://doi.org/10.1090/proc/16296