Well-posedness and global existence for a generalized Degasperis–Procesi equation. (April 2016)

• Record Type: Journal Article
• Authors: Li, Jinlu; Yin, Zhaoyang
• Is Part Of: Nonlinear analysis. Volume 28(2016)
• Page Start: 72
• Page End: 90
• Publication Date: 2016-04
• Subjects: A generalized Degasperis–Procesi equation -- Littlewood–Paley theory -- Local well-posedness -- Blow-up criterion -- Global existence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.09.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We first establish the local existence and uniqueness of strong solutions for the Cauchy problem of a generalized Degasperis–Procesi equation in nonhomogeneous Besov spaces by using the Littlewood–Paley theory. Then, we prove the solution depends continuously on the initial data. Finally, we derive a blow-up criterion and present a global existence result for the equation.