Limiting profile of the blow-up solutions for the fourth-order nonlinear Schrödinger equation

Abstract

This paper is concerned with the blow-up solutions of the focusing fourth-order mass-critical nonlinear Schrödinger equation. Establishing the profile decomposition of the bounded sequences in H2, we obtain the variational characteristics of the corresponding ground state and a compactness lemma. Moreover, we obtain the L2-concentration of the blow-up solutions and the limiting profile of the minimal mass blow-up solutions in the general case. © 2010 International Press.