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On blow-up criterion for the nonlinear Schrödinger equation

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  • The blowup is studied for the nonlinear Schrödinger equation $iu_{t}+\Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $p\ge 1+\frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative energy $E(u_0)<0$ blows up in finite or infinite time. A new proof is also presented for the previous result in [9], in which a similar result in a case of energy-subcritical was shown.
    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B44.


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