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Local well-posedness and time regularity for a fifth-order shallow water equations in analytic Gevrey–Bourgain spaces
Monatshefte für Mathematik ( IF 0.9 ) Pub Date : 2020-09-22 , DOI: 10.1007/s00605-020-01464-x
Aissa Boukarou , Kaddour Guerbati , Khaled Zennir

This paper studies a Cauchy problems for fifth-order shallow water equations with nonlinear terms in (1). With data in analytic Gevrey spaces on the line, we prove that the problem is well defined. We also treat the regularity in time which belongs to \(G^{5\sigma }\) near zero for every x on the line. The proof is based mainly on bilinear and trilinear estimates in the analytic Gevrey–Bourgain spaces, relies on the contraction mapping theorem to improve the results in Jia and Huo (J Differ Equ 246:2448–2467, 2009).



中文翻译:

解析Gevrey-Bourgain空间中五阶浅水方程的局部适定性和时间规律

本文研究(1)中带有非线性项的五阶浅水方程的柯西问题。利用在线的分析Gevrey空间中的数据,我们证明了问题已得到很好的定义。对于行中的每个x,我们还处理属于\(G ^ {5 \ sigma} \)的时间规律性。证明主要基于解析Gevrey-Bourgain空间中的双线性和三线性估计,并依靠收缩映射定理来改进Jia和Huo的结果(J Differ Equ 246:2448-2467,2009)。

更新日期:2020-09-22
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