On the existence and uniqueness of smooth solution for a generalized Zakharov equation

The paper deals with the existence and uniqueness of smooth solution for a generalized Zakharov equation. We establish local in time existence and uniqueness in the case of dimension d = 2 , 3 . Moreover, by using the conservation laws and Brezis–Gallouet inequality, the solution can be extended glo...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2010-05, Vol.365 (1), p.238-253
Main Authors: Guo, Boling, Zhang, Jingjun, Pu, Xueke
Format: Article
Language:English
Subjects:
Generalized Zakharov equation
Self-generated magnetic field
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Summary:The paper deals with the existence and uniqueness of smooth solution for a generalized Zakharov equation. We establish local in time existence and uniqueness in the case of dimension d = 2 , 3 . Moreover, by using the conservation laws and Brezis–Gallouet inequality, the solution can be extended globally in time in two dimensional case for small initial data. Besides, we also prove global existence of smooth solution in one spatial dimension without any small assumption for initial data.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.10.045