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

Van Duong Dinh

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arXiv · 1801.08866

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

Van Duong Dinh

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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.

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Van Duong Dinh. 2018-01-25. On blowup solutions to the focusing intercritical nonlinear fourth-order Schr\"odinger equation. https://arxiv.org/abs/1801.08866

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