Dynamics of Partial Differential Equations
Volume 20 (2023)
Blow-up or Grow-up for the threshold solutions to the nonlinear Schrödinger equation
Pages: 213 – 225
We consider the nonlinear Schrödinger equation with $L^2$-supercritical and $H^1$-subcritical power type nonlinearity. Duyckaerts and Roudenko  and Campos, Farah, and Roudenko  studied the global dynamics of the solutions with same mass and energy as that of the ground state. In these papers, finite variance is assumed to show the finite time blow-up. In the present paper, we remove the finite-variance assumption and prove a blow-up or grow-up result.
nonlinear Schrödinger equation, blow-up, grow-up, threshold
2010 Mathematics Subject Classification
Primary 35Q55. Secondary 35B44.
Research of the first author is partially supported by an NSERC Discovery Grant. The second author is supported by JSPS Overseas Research Fellowship and KAKENHI Grant-in-Aid for Early-Career Scientists No. JP18K13444.
Received 11 January 2023
Published 19 May 2023