The well posedness of the dissipative Korteweg–de Vries equations with low regularity data

✍ Scribed by Jinsheng Han; Lizhong Peng

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 365 KB
• Volume: 69
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.05.008

✦ Synopsis

We study the Cauchy problem of a dissipative version of the KdV equation with rough initial data. By working in a Bourgain type space we prove the local and global well posedness results for Sobolev spaces of negative order, and the order number is lower than the well known value -3 4 . In some sense this paper is intended to show how the Bourgain type space is applicable to the study of semilinear equations with a linear part which contain both dissipative and dispersive terms.