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Blow-up of $ H\sp 1$ solutions for the one-dimensional nonlinear Schrödinger equation with critical power nonlinearity


Authors: Takayoshi Ogawa and Yoshio Tsutsumi
Journal: Proc. Amer. Math. Soc. 111 (1991), 487-496
MSC: Primary 35B05; Secondary 35Q55
DOI: https://doi.org/10.1090/S0002-9939-1991-1045145-5
MathSciNet review: 1045145
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Abstract: We investigate the blow-up of solutions in $ {H^1}({\mathbf{R}})$ with negative energy for the one-dimensional nonlinear Schrödinger equation with critical power nonlinearity:

\begin{displaymath}\begin{gathered}i{u_t} = - {u_{xx}} - \vert u{\vert^4}u,\quad... ...= {u_0}(x),\quad x \in {\mathbf{R}}. \hfill \\ \end{gathered} .\end{displaymath}

In our result we remove the weight condition $ x{u_0} \in {L^2}({\mathbf{R}})$, which was always assumed to show the blow-up of solutions in the previous papers.

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DOI: https://doi.org/10.1090/S0002-9939-1991-1045145-5
Article copyright: © Copyright 1991 American Mathematical Society

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