On blowup solutions to the focusing intercritical nonlinear fourth-order Schrödinger equation

Published 25 Jan 2018 in math.AP | (1801.08866v3)

Abstract: In this paper we study dynamical properties of blowup solutions to the focusing intercritical (mass-supercritical and energy-subcritical) nonlinear fourth-order Schr\"odinger equation. We firstly establish the profile decomposition of bounded sequences in $\dot{H}^{{\gamma_{\text{c}}}} \cap \dot{H}^2$. We also prove a compactness lemma and a variational characterization of ground states related to the equation. As a result, we obtain the $\dot{H}^{{\gamma_{\text{c}}}$-concentration} of blowup solutions with bounded $\dot{H}^{{\gamma_{\text{c}}}$-norm} and the limiting profile of blowup solutions with critical $\dot{H}^{{\gamma_{\text{c}}}$-norm.}