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Global Solutions and Stability Properties of the 5th Order Gardner Equation
Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2021-06-17 , DOI: 10.1007/s10884-021-10022-4
Miguel A. Alejo , Chulkwang Kwak

In this work, we deal with the initial value problem of the 5th-order Gardner equation in \({\mathbb {R}}\), presenting the local well-posedness result in \(H^2({\mathbb {R}})\). As a consequence of the local result, in addition to \(H^2\)-energy conservation law, we are able to prove the global well-posedness result in \(H^2({\mathbb {R}})\). Finally as a direct application, we prove that some globally defined functions, e.g. breather solutions of 5th order Gardner equation, are \(H^2({\mathbb {R}})\) stable.



中文翻译:

五阶 Gardner 方程的全局解和稳定性性质

在这项工作中,我们处理\({\mathbb {R}}\)中的五阶 Gardner 方程的初值问题,在\(H^2({\mathbb {R }})\)。作为局部结果的结果,除了\(H^2\) -能量守恒定律之外,我们还能够证明\(H^2({\mathbb {R}})\ )。最后作为一个直接的应用,我们证明了一些全局定义的函数,例如5 阶Gardner 方程的呼吸解,是\(H^2({\mathbb {R}})\)稳定的。

更新日期:2021-06-18
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