Well-posedness and ill-posedness of KdV equation with higher dispersion

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Li, Yin^1,3  Yan, Wei² 

[1] Shaoguan Univ, Sch Math & Informat Sci, Shaoguan 512005, Peoples R China

[2] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[3] Sun Yat Sen Univ, Dept Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

关键词: KdV equation with 2n+1 order dispersion;    Well-posedness and ill-posedness;    Fourier restriction norm method;   

DOI  :  10.1016/j.jmaa.2014.01.035

来源: Elsevier

【 摘 要 】

First, the Cauchy problem for KdV equation with 2n +1 order dispersion is studied, and the local well-posedness result for the initial data in Sobolev spaces H-S (R) with s > -n + 1/4 is established via the Fourier restriction norm method. Second, we prove 4 that the KdV equation with 2n + 1 order dispersion is ill-posed for the initial data in H-s (R) with s < -n + 1/4, n >= 2, n is an element of N+ if the flow map is C-2 differentiable at zero form H-s(R) to C([0,T]; H-s(R)). Finally, we obtain the sharp regularity requirement for the KdV equation with 2n + 1 order dispersion s > -n + 1/4. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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