On blowup solutions to the focusing intercritical nonlinear fourth-order Schr\"odinger equation

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.