Gevrey regularity of the periodic gKdV equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Hannah, Heather²  Himonas, A. Alexandrou¹  Petronilho, Gerson³ 

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] E Cent Univ, Dept Math, Ada, OK 74820 USA

[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil

关键词: Generalized Korteweg-de Vries equation gKdV;    Initial value problem;    Periodic;    Gevrey regularity;    Multilinear estimates;    Sobolev spaces;   

DOI  :  10.1016/j.jde.2010.12.020

来源: Elsevier

【 摘 要 】

Using the multilinear estimates, which were derived for proving well-posedness of the generalized Korteweg-de Vries (gKdV) equation, it is shown that if the initial data belongs to Gevrey space G(sigma), sigma >= 1, in the space variable then the solution to the corresponding Cauchy problem for gKdV belongs also to G(sigma) in the space variable. Moreover, the solution is not necessarily G(sigma) in the time variable. However, it belongs to G(3 sigma) near 0. When sigma = 1 these are analytic regularity results for gKdV. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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