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    The existence of global strong and weak solutions for the Novikov equation

    Access Status
    Open access via publisher
    Authors
    Lai, Shaoyong
    Li, Nan
    Wu, Yong Hong
    Date
    2013
    Type
    Journal Article
    
    Metadata
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    Citation
    Lai, Shaoyong and Li, Nan and Wu, Yonghong. 2013. The existence of global strong and weak solutions for the Novikov equation. Journal of Mathematical Analysis and Applications. 399 (2): pp. 682-691.
    Source Title
    Journal of Mathematical Analysis and Applications
    DOI
    10.1016/j.jmaa.2012.10.048
    ISSN
    0022247X
    URI
    http://hdl.handle.net/20.500.11937/39165
    Collection
    • Curtin Research Publications
    Abstract

    The well-posedness of the global strong and weak solutions for the Novikov equation is investigated. Provided that initial value u0 ∈ Hs(s > 3/2) and satisfying a sign condition, the existence and uniqueness of global strong solutions for the equation are shown to be valid in Sobolev space. The estimates in Hq(R) space with 0≤q≤1/2, which are derived from the equation itself, are developed to prove the existence and uniqueness of the global weak solutions.

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