Blow-up of $H^ 1$ solutions for the one-dimensional nonlinear Schrödinger equation with critical power nonlinearity
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- by Takayoshi Ogawa and Yoshio Tsutsumi PDF
- Proc. Amer. Math. Soc. 111 (1991), 487-496 Request permission
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: \[ \begin {gathered} i{u_t} = - {u_{xx}} - |u{|^4}u,\quad t > 0,x \in {\mathbf {R}}, \hfill \\ u(0,x) = {u_0}(x),\quad x \in {\mathbf {R}}. \hfill \\ \end {gathered} .\] 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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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