On blow-up criterion for the nonlinear Schrödinger equation

The blowup is studied for the nonlinear Schrödinger equationiuₜ+Δ u+ |u|ᵖ⁻¹u=0 with p is odd and p≥ 1+ 4N-2 (theenergy-critical or energy-supercritical case). It is shown that thesolution with negative energy E(u₀)<0 blows up in finite orinfinite time. A new proof is also presented for the previous resultin [9], in which a similar result in acase of energy-subcritical was shown.