Domain and range of the modified wave operator for schrödinger equations with a critical nonlinearity

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We study the final problem for the nonlinear Schrödinger equation itu+ 1/2 Δu = λ|u|2/nu, (t,x)∈ R × Rn where λ ∈ R,n =1,2,3. If the final data u + ∈ H0,α = {φ ∈ L2 :( 1+|x|)α φ ∈ L2}with n/2 < α < min( n, 2,1+2/n) and the norm ∥û+∥L ∞t is sufficiently small, then we prove the existence of the wave operator in L 2. We also construct the modified scattering operator from H 0,α to H 0,δ with n/2 < δ < α.

Original languageEnglish
Pages (from-to)477-492
Number of pages16
JournalCommunications in Mathematical Physics
Volume267
Issue number2
DOIs
Publication statusPublished - 2006 Oct 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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