Global, small radially symmetric solutions to nonlinear Schrödinger equations and a gauge transformation

Nakao Hayashi, Tohru Ozawa, Roger Temam

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12 Citations (Scopus)


This paper proves the global existence of small radially symmetric solutions to the nonlinear Schrödinger equations of the form (i∂tu + 1/2Δu = F(u,∇u, u,∇u), (t, x) ∈ R x Rn, u(0, x) = ε0Φ(|x|), x ∈ Rn, where n ≥ 3, ∈0 is sufficiently small, |x| = with λαα,β l1, l2, l3 ∈ N, l0 = 3 for n = 3, 4, and l0 = 2 for n ≥ 5. The method depends on the combination of a gauge transformation and generalized energy estimtes and does not require the condition such that ∂∇uF is pure imaginary which is needed for the classical energy method.

Original languageEnglish
Pages (from-to)1061-1072
Number of pages12
JournalDifferential and Integral Equations
Issue number5
Publication statusPublished - 1995
Externally publishedYes


ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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