Vol. 8, No. 8, 2015

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Well-posedness and scattering for the Zakharov system in four dimensions

Ioan Bejenaru, Zihua Guo, Sebastian Herr and Kenji Nakanishi

Vol. 8 (2015), No. 8, 2029–2055
Abstract

The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are proved, including the case of initial data in the energy space. None of these results are restricted to radially symmetric data.

Keywords
nonlinear wave equation, nonlinear Schrödinger equation, Zakharov system, well-posedness, scattering
Mathematical Subject Classification 2010
Primary: 35L70, 35Q55
Milestones
Received: 4 April 2015
Accepted: 3 September 2015
Published: 23 December 2015
Authors
Ioan Bejenaru
Department of Mathematics
University of California, San Diego
9500 Gilman Dr
La Jolla, CA 92093-0112
United States
Zihua Guo
School of Mathematical Sciences
Monash University
Melbourne VIC 3800
Australia
LMAM
School of Mathematical Sciences
Peking University
Beijing 100871
China
Sebastian Herr
Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
D-33501 Bielefeld
Germany
Kenji Nakanishi
Department of Pure and Applied Mathematics
Osaka University
Graduate School of Information Science and Technology
Osaka 560-0043
Japan