Well-posedness result for the Ostrovsky, Stepanyams and Tsimring equation at the critical regularity. (December 2018)

• Record Type: Journal Article
• Authors: Wang, Hongwei; Esfahani, Amin
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 347
• Page End: 364
• Publication Date: 2018-12
• Subjects: OST equation -- Cauchy problem -- Critical regularity -- Besov–Bourgain space; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.05.011
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Studied here is the Ostrovsky, Stepanyams and Tsimring (OST) equation u t + u x x x − ε H ( u + u x x ) x + u u x = 0 . It is showed that the associated initial value problem is locally analytically well-posed in the critical Sobolev spaces H − 3 ∕ 2 ( R ) . This improves the previous results on this equation in the Sobolev spaces.