On Blow-up criterion for the Nonlinear Schrödinger Equation

Abstract

The blowup is studied for the nonlinear Schrödinger equation $i{u}_t+\Delta u+|u{|}^{p-1}u=0$ 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 \cite{HoRo2}, in which a similar result but more general in a case of energy-subcritical was shown.

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References in corpus (1)

• Nonscattering solutions to the $L^2$-supercritical NLS Equations

Cited by in corpus (3)

• Global Dynamics below the standing waves for the focusing semilinear Schrödinger equation with a repulsive Dirac delta potential
• Global Dynamics of solutions with group invariance for the nonlinear Schrödinger equation
• Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space