The focusing energy-critical fourth-order Schrödinger equationwith radial data

Benoît Pausader

doi:10.3934/dcds.2009.24.1275

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2009, Volume 24, Issue 4: 1275-1292. Doi: 10.3934/dcds.2009.24.1275

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

Benoît Pausader^1,

1.
Department of Mathematics, University of Cergy-Pontoise, CNRS UMR 8088, 2, avenue Adolphe Chauvin, 95302 CERGY-PONTOISE cedex

Received: April 30, 2008

Revised: August 31, 2008

Published: October 2009

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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.

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Mathematics Subject Classification: 35Q40, 35Q55.

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