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

Abstract

In this paper we study dynamical properties of blowup solutions to the focusing intercritical (mass-supercritical and energy-subcritical) nonlinear fourth-order Schrödinger 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.

arXiv comment27 pages, revised version to appear J. Dynam. Differential Equations