Local Well-posedness and Persistence Property for the Generalized Novikov Equation

Yongye Zhao; Yongsheng Li; Wei Yan

doi:10.3934/dcds.2014.34.803

Article Contents

2014, Volume 34, Issue 2: 803-820. Doi: 10.3934/dcds.2014.34.803

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Local Well-posedness and Persistence Property for the Generalized Novikov Equation

1.
Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640
2.
College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007

Received: November 30, 2012

Revised: January 31, 2013

Published: January 2014

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Abstract

In this paper, we study the generalized Novikov equation which describes the motion of shallow water waves. By using the Littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the generalized Novikov equation is locally well-posed in Besov space $B_{p,r}^{s}$ with $1\leq p, r\leq +\infty$ and $s>{\rm max}\{1+\frac{1}{p},\frac{3}{2}\}$. We also show the persistence property of the strong solutions which implies that the solution decays at infinity in the spatial variable provided that the initial function does.

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Mathematics Subject Classification: Primary: 35Q53, 35G25; Secondary: 35B30, 35A35.

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