Blow-up of H1 solution for the nonlinear Schrödinger equation

Takayoshi Ogawa, Yoshio Tsutsumi

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214 Citations (Scopus)


We consider the blow-up of the solution in H1 for the following nonlinear Schrödinger equation: i ∂ ∂tu + Δu = -|u|p - 1u, x ε{lunate} Rn, t ≥ 0, (*) u(0, x) = u0(X), x ε{lunate} Rn, t = 0, where n ≥2 and 1 + 4/n ≤ p < min { (n + 2) (n - 2), 5}. We prove that if the initial data u0 in H1 are radially symmetric and have negative energy, then the solution of (*) in H1 blows up in finite time. We do not assume that xu0 ε{lunate} L2, and therefore our result is the generalization of the results of Glassey [4] and M. Tsutsumi [18] for the radially symmetric case.

Original languageEnglish
Pages (from-to)317-330
Number of pages14
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - 1991 Aug


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