Non-radial finite time blow-up for the fourth-order nonlinear Schrödinger equations

van Duong Dinh (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We revisit the finite time blow-up for the fourth-order Schrödinger equation with focusing inhomogeneous nonlinearity −|x| −2 |u| 4 n u. By exploiting localized virial estimates and spatial decay of the nonlinearity, we prove the finite time blow-up of non-radial solutions with negative energy. Our result is the first one dealing with the existence of non-radial blow-up solutions to the fourth-order Schrödinger equations.

Mots clés: Fourth-order nonlinear Schrödinger equation; Blow-up

Domaines: Equations aux dérivées partielles [math.AP]

van Duong Dinh. Non-radial finite time blow-up for the fourth-order nonlinear Schrödinger equations. Applied Mathematics Letters, In press, ⟨10.1016/j.aml.2022.108084⟩. ⟨hal-03629255⟩