The Cauchy problem of a periodic higher order KdV equation in analytic Gevrey spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Gorsky, J.¹  Himonas, A. Alexandrou²  Holliman, C.³  Petronilho, G.⁴ 

[1] Univ San Diego, Dept Math & Comp Sci, San Diego, CA 92110 USA

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

[3] Univ Alabama Birmingham, Dept Biostat, Birmingham, AL 35294 USA

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

关键词: KdV equation;    Higher dispersion;    Initial value problem;    Well-posedness;    Analytic Gevrey spaces;    Uniform radius of analyticity;    Sobolev spaces;    Bilinear estimates;    Bourgain spaces;   

DOI  :  10.1016/j.jmaa.2013.04.015

来源: Elsevier

【 摘 要 】

This paper studies the periodic Cauchy problem for a KdV equation whose dispersion is of order m = 2j + 1, where j is a positive integer, (KdVm). Using Bourgain-Gevrey type analytic spaces and appropriate bilinear estimates, it is shown that local in time well-posedness holds when the initial data belong to an analytic Gevrey spaces of order sigma. This implies that in the space variable the regularity of the solution remains the same with that of the initial data. It also implies that the size of the uniform radius of analyticity is preserved. Moreover, the solution is not necessarily G(sigma) in time. However, it belongs to G(m sigma) (R) near zero for every x on the circle. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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