On the ill-posedness of the Gardner equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Alejo, Miguel A.¹ 

[1] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen, Denmark

关键词: Gardner equation;    Breather;    Ill-posedness;    Integrability;   

DOI  :  10.1016/j.jmaa.2012.06.018

来源: Elsevier

【 摘 要 】

We present ill-posedness results for the initial value problem (IVP) for the Gardner equation. We measure the regularity of the Cauchy problem in the classical Sobolev spaces H-s, and show the critical Sobolev index under which the local well-posedness of the problem is not present, in the sense that the dependence of solutions upon initial data fails to be continuous. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free