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 λα,λα,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.
|ジャーナル||Differential and Integral Equations|
|出版ステータス||Published - 1995|
ASJC Scopus subject areas
- Applied Mathematics