Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

The focusing energy-critical fourth-order Schrödinger equation with radial data

Pages: 1275 - 1292, Volume 24, Issue 4, August 2009      doi:10.3934/dcds.2009.24.1275

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Benoît Pausader - Department of Mathematics, University of Cergy-Pontoise, CNRS UMR 8088, 2, avenue Adolphe Chauvin, 95302 CERGY-PONTOISE cedex, France (email)

Abstract: In this paper, we investigate the focusing energy-critical fourth-order Schrödinger equation in the radial setting. We prove global existence and scattering for solutions of energy and $\dot{H}^2$-norm below that of the ground state.

Keywords:  Fourth-order Schrödinger equation, nonlinear dispersive equation, focusing equation, nonlinear scattering.
Mathematics Subject Classification:  35Q40, 35Q55.

Received: May 2008;      Revised: September 2008;      Available Online: May 2009.