The existence of global strong and weak solutions for the Novikov equation
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2013Type
Journal Article
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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.
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Journal of Mathematical Analysis and Applications
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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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