The Cauchy problem for Kawahara equation in Sobolev spaces with low regularity |
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Authors: | Wei Yan Yongsheng Li |
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Affiliation: | Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, People's Republic of China |
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Abstract: | This paper is devoted to studying the initial‐value problem of the Kawahara equation. By establishing some crucial bilinear estimates related to the Bourgain spaces Xs, b(R2) introduced by Bourgain and homogeneous Bourgain spaces, which is defined in this paper and using I‐method as well as L2 conservation law, we show that this fifth‐order shallow water wave equation is globally well‐posed for the initial data in the Sobolev spaces Hs(R) with $s{>}-frac{63}{58}$. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | Cauchy problem global well‐posedness Kawahara equation Bourgain spaces |
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