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Well-posedness and
scattering for the Zakharov system in four dimensions
Ioan Bejenaru, Zihua Guo, Sebastian Herr and Kenji Nakanishi |
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Vol. 8 (2015), No. 8, 2029–2055
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 35L70, 35Q55
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Milestones
Received: 4 April 2015
Accepted: 3 September 2015
Published: 23 December 2015
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Authors |
| Ioan Bejenaru | |
| Department of Mathematics University of California, San Diego 9500 Gilman Dr La Jolla, CA 92093-0112 United States |
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| 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 |
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| Kenji Nakanishi | |
| Department of Pure and Applied
Mathematics Osaka University Graduate School of Information Science and Technology Osaka 560-0043 Japan |
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