Blow-up of rough solutions to the fourth-order nonlinear Schrödinger equation

This paper deals with the formation of singularities of rough blow-up solutions to the fourth-order nonlinear Schrödinger equation. The limiting profile and L2L2-concentration of the rough blow-up solutions are obtained in Hs(R4)Hs(R4) with s>s0s>s0, where s0≤9+72120≈1.793. The new ingredient relies on the refined compactness result developed by Zhu et al. [S.H. Zhu, J. Zhang, H. Yang, Limiting profile of the blow-up solutions for the fourth-order nonlinear Schrödinger equation, Dyn. Partial Differ. Equ. 7 (2010) 187–205].